Closed Form Solution Linear Regression

  closed form solution linear regression: Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow Aurélien Géron, 2019-09-05 Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. Now, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how. By using concrete examples, minimal theory, and two production-ready Python frameworks—Scikit-Learn and TensorFlow—author Aurélien Géron helps you gain an intuitive understanding of the concepts and tools for building intelligent systems. You’ll learn a range of techniques, starting with simple linear regression and progressing to deep neural networks. With exercises in each chapter to help you apply what you’ve learned, all you need is programming experience to get started. Explore the machine learning landscape, particularly neural nets Use Scikit-Learn to track an example machine-learning project end-to-end Explore several training models, including support vector machines, decision trees, random forests, and ensemble methods Use the TensorFlow library to build and train neural nets Dive into neural net architectures, including convolutional nets, recurrent nets, and deep reinforcement learning Learn techniques for training and scaling deep neural nets
  closed form solution linear regression: Probability and Statistics for Machine Learning Charu C. Aggarwal,
  closed form solution linear regression: Machine Learning Fundamentals Hui Jiang, 2021-11-25 A coherent introduction to core concepts and deep learning techniques that are critical to academic research and real-world applications.
  closed form solution linear regression: An Introduction to Machine Learning Gopinath Rebala, Ajay Ravi, Sanjay Churiwala, 2019-05-07 Just like electricity, Machine Learning will revolutionize our life in many ways – some of which are not even conceivable today. This book provides a thorough conceptual understanding of Machine Learning techniques and algorithms. Many of the mathematical concepts are explained in an intuitive manner. The book starts with an overview of machine learning and the underlying Mathematical and Statistical concepts before moving onto machine learning topics. It gradually builds up the depth, covering many of the present day machine learning algorithms, ending in Deep Learning and Reinforcement Learning algorithms. The book also covers some of the popular Machine Learning applications. The material in this book is agnostic to any specific programming language or hardware so that readers can try these concepts on whichever platforms they are already familiar with. Offers a comprehensive introduction to Machine Learning, while not assuming any prior knowledge of the topic; Provides a complete overview of available techniques and algorithms in conceptual terms, covering various application domains of machine learning; Not tied to any specific software language or hardware implementation.
  closed form solution linear regression: Materials Data Science Stefan Sandfeld,
  closed form solution linear regression: Kernel Methods in Computer Vision Christoph H. Lampert, 2009 Few developments have influenced the field of computer vision in the last decade more than the introduction of statistical machine learning techniques. Particularly kernel-based classifiers, such as the support vector machine, have become indispensable tools, providing a unified framework for solving a wide range of image-related prediction tasks, including face recognition, object detection and action classification. By emphasizing the geometric intuition that all kernel methods rely on, Kernel Methods in Computer Vision provides an introduction to kernel-based machine learning techniques accessible to a wide audience including students, researchers and practitioners alike, without sacrificing mathematical correctness. It covers not only support vector machines but also less known techniques for kernel-based regression, outlier detection, clustering and dimensionality reduction. Additionally, it offers an outlook on recent developments in kernel methods that have not yet made it into the regular textbooks: structured prediction, dependency estimation and learning of the kernel function. Each topic is illustrated with examples of successful application in the computer vision literature, making Kernel Methods in Computer Vision a useful guide not only for those wanting to understand the working principles of kernel methods, but also for anyone wanting to apply them to real-life problems.
  closed form solution linear regression: Hands-On Machine Learning with Scikit-Learn and TensorFlow Aurélien Géron, 2017-03-13 Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. Now, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how. By using concrete examples, minimal theory, and two production-ready Python frameworks--scikit-learn and TensorFlow--author Aurélien Géron helps you gain an intuitive understanding of the concepts and tools for building intelligent systems. You'll learn a range of techniques, starting with simple linear regression and progressing to deep neural networks. With exercises in each chapter to help you apply what you've learned, all you need is programming experience to get started.
  closed form solution linear regression: Econometric Methods with Applications in Business and Economics Christiaan Heij, Paul de Boer, Philip Hans Franses, Teun Kloek, Herman K. van Dijk, All at the Erasmus University in Rotterdam, 2004-03-25 Nowadays applied work in business and economics requires a solid understanding of econometric methods to support decision-making. Combining a solid exposition of econometric methods with an application-oriented approach, this rigorous textbook provides students with a working understanding and hands-on experience of current econometrics. Taking a 'learning by doing' approach, it covers basic econometric methods (statistics, simple and multiple regression, nonlinear regression, maximum likelihood, and generalized method of moments), and addresses the creative process of model building with due attention to diagnostic testing and model improvement. Its last part is devoted to two major application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and the econometrics of time series data (univariate time series, trends, volatility, vector autoregressions, and a brief discussion of SUR models, panel data, and simultaneous equations). · Real-world text examples and practical exercise questions stimulate active learning and show how econometrics can solve practical questions in modern business and economic management. · Focuses on the core of econometrics, regression, and covers two major advanced topics, choice data with applications in marketing and micro-economics, and time series data with applications in finance and macro-economics. · Learning-support features include concise, manageable sections of text, frequent cross-references to related and background material, summaries, computational schemes, keyword lists, suggested further reading, exercise sets, and online data sets and solutions. · Derivations and theory exercises are clearly marked for students in advanced courses. This textbook is perfect for advanced undergraduate students, new graduate students, and applied researchers in econometrics, business, and economics, and for researchers in other fields that draw on modern applied econometrics.
  closed form solution linear regression: Multi-way Analysis Age Smilde, Rasmus Bro, Paul Geladi, 2005-06-10 This book is an introduction to the field of multi-way analysis for chemists and chemometricians. Its emphasis is on the ideas behind the method and its pratical applications. Sufficient mathematical background is given to provide a solid understanding of the ideas behind the method. There are currently no other books on the market which deal with this method from the viewpoint of its applications in chemistry. Applicable in many areas of chemistry. No comparable volume currently available. The field is becoming increasingly important.
  closed form solution linear regression: Classification and Knowledge Organization Rüdiger Klar, Otto Opitz, 2013-03-14 Large collections of data and information necessitate adequate methods for their analysis. The book presents such methods, proposes and discusses recent approaches and implementations and describes a series of practical applications.
  closed form solution linear regression: Predictions, Nonlinearities and Portfolio Choice Friedrich Christian Kruse, 2012 Finance researchers and asset management practitioners put a lot of effort into the question of optimal asset allocation. With this respect, a lot of research has been conducted on portfolio decision making as well as quantitative modeling and prediction models. This study brings together three fields of research, which are usually analyzed in an isolated manner in the literature: - Predictability of asset returns and their covariance matrix - Optimal portfolio decision making - Nonlinear modeling, performed by artificial neural networks, and their impact on predictions as well as optimal portfolio construction Including predictability in asset allocation is the focus of this work and it pays special attention to issues related to nonlinearities. The contribution of this study to the portfolio choice literature is twofold. First, motivated by the evidence of linear predictability, the impact of nonlinear predictions on portfolio performances is analyzed. Predictions are empirically performed for an investor who invests in equities (represented by the DAX index), bonds (represented by the REXP index) and a risk-free rate. Second, a solution to the dynamic programming problem for intertemporal portfolio choice is presented. The method is based on functional approximations of the investor's value function with artificial neural networks. The method is easily capable of handling multiple state variables. Hence, the effect of adding predictive parameters to the state space is the focus of analysis as well as the impacts of estimation biases and the view of a Bayesian investor on intertemporal portfolio choice. One important empirical result shows that residual correlation among state variables have an impact on intertemporal portfolio decision making.
  closed form solution linear regression: Linear Algebra and Optimization for Machine Learning Charu C. Aggarwal, 2020-05-13 This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout the book. A solution manual for the exercises at the end of each chapter is available to teaching instructors. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows: 1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts. 2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning.
  closed form solution linear regression: Clinical Trial Data Analysis Using R Ding-Geng (Din) Chen, Karl E. Peace, 2010-12-14 Too often in biostatistical research and clinical trials, a knowledge gap exists between developed statistical methods and the applications of these methods. Filling this gap, Clinical Trial Data Analysis Using R provides a thorough presentation of biostatistical analyses of clinical trial data and shows step by step how to implement the statistical methods using R. The book’s practical, detailed approach draws on the authors’ 30 years of real-world experience in biostatistical research and clinical development. Each chapter presents examples of clinical trials based on the authors’ actual experiences in clinical drug development. Various biostatistical methods for analyzing the data are then identified. The authors develop analysis code step by step using appropriate R packages and functions. This approach enables readers to gain an understanding of the analysis methods and R implementation so that they can use R to analyze their own clinical trial data. With step-by-step illustrations of R implementations, this book shows how to easily use R to simulate and analyze data from a clinical trial. It describes numerous up-to-date statistical methods and offers sound guidance on the processes involved in clinical trials.
  closed form solution linear regression: Case Studies in Bayesian Statistical Modelling and Analysis Clair L. Alston, Kerrie L. Mengersen, Anthony N. Pettitt, 2012-10-10 Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing. Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.
  closed form solution linear regression: Intelligent Computing: An Introduction to Artificial Intelligence Book Dr. Shivamurthaiah M , Dr. Praveen Kumar K, Dr. Vinay S, Prof. Rakesh Podaralla, 2023-10-20 In this book named ‘Intelligent Computing: An Introduction to Artificial Intelligence.’ the authors try to give detailed information on various aspects of Intelligent computing. This book consists of seven chapters from Introduction to AI to the Future of AI. The first chapter consists of the Introduction, history importance, and impact of intelligent computing in various fields. The Second chapter gives information about the Foundations of Artificial Intelligence which is cognitive science and its relation to AI. It also explains the Key concepts of Machine learning, Neural networks, Natural language processing and followed by concepts of Robotics. The third chapter explains Intelligent Computing Techniques named Supervised learning: Linear regression, Logistic regression, Support vector machines, Unsupervised learning: Clustering algorithms, Dimensionality reduction, Association rule mining, Deep learning: Neural network architectures, Convolutional neural networks, Recurrent neural networks: Generative adversarial networks, Reinforcement learning, Markov decision processes, Q-learning, Deep reinforcement learning. The fourth chapter consists of information about Applications of Intelligent Computing. Natural language processing applications: Sentiment analysis, Speech recognition, Machine translation, Computer vision applications like Object detection and recognition, Image classification, Facial recognition, Robotics applications Like Autonomous Vehicles, Industrial Automation, human robots, Healthcare applications, Disease diagnosis, Medical Image Analysis & Drug discovery. The fifth chapter consists of topics on the Ethical and Social prospective of the Implications of Intelligent Computing covers the Limitations & strengths of AI algorithms, Privacy and security concerns, Automation and its impact on job displacement also about governance and regulations on AI by the government. The sixth Chapter contains Future Directions and Challenges in Intelligent Computing Advances like interpretability of AI systems, Human-AI collaboration and augmentation, and Addressing ethical and societal challenges. The last chapter gives a conclusion about the topic: key points of AI, its Potential impact in the future & required Encouragement for further exploration of AI and intelligent computing. This book gives detailed enough information for the reader to enhance their knowledge of Intelligent Computing and AI.
  closed form solution linear regression: Computational Intelligence in Data Mining - Volume 2 Lakhmi C. Jain, Himansu Sekhar Behera, Jyotsna Kumar Mandal, Durga Prasad Mohapatra, 2014-12-10 The contributed volume aims to explicate and address the difficulties and challenges that of seamless integration of the two core disciplines of computer science, i.e., computational intelligence and data mining. Data Mining aims at the automatic discovery of underlying non-trivial knowledge from datasets by applying intelligent analysis techniques. The interest in this research area has experienced a considerable growth in the last years due to two key factors: (a) knowledge hidden in organizations’ databases can be exploited to improve strategic and managerial decision-making; (b) the large volume of data managed by organizations makes it impossible to carry out a manual analysis. The book addresses different methods and techniques of integration for enhancing the overall goal of data mining. The book helps to disseminate the knowledge about some innovative, active research directions in the field of data mining, machine and computational intelligence, along with some current issues and applications of related topics.
  closed form solution linear regression: Large-Scale Data Analytics with Python and Spark Isaac Triguero, Mikel Galar, 2023-11-23 Based on the authors' extensive teaching experience, this hands-on graduate-level textbook teaches how to carry out large-scale data analytics and design machine learning solutions for big data. With a focus on fundamentals, this extensively class-tested textbook walks students through key principles and paradigms for working with large-scale data, frameworks for large-scale data analytics (Hadoop, Spark), and explains how to implement machine learning to exploit big data. It is unique in covering the principles that aspiring data scientists need to know, without detail that can overwhelm. Real-world examples, hands-on coding exercises and labs combine with exceptionally clear explanations to maximize student engagement. Well-defined learning objectives, exercises with online solutions for instructors, lecture slides, and an accompanying suite of lab exercises of increasing difficulty in Jupyter Notebooks offer a coherent and convenient teaching package. An ideal teaching resource for courses on large-scale data analytics with machine learning in computer/data science departments.
  closed form solution linear regression: Foundations of Predictive Analytics James Wu, Stephen Coggeshall, 2012-02-15 Drawing on the authors’ two decades of experience in applied modeling and data mining, Foundations of Predictive Analytics presents the fundamental background required for analyzing data and building models for many practical applications, such as consumer behavior modeling, risk and marketing analytics, and other areas. It also discusses a variety of practical topics that are frequently missing from similar texts. The book begins with the statistical and linear algebra/matrix foundation of modeling methods, from distributions to cumulant and copula functions to Cornish–Fisher expansion and other useful but hard-to-find statistical techniques. It then describes common and unusual linear methods as well as popular nonlinear modeling approaches, including additive models, trees, support vector machine, fuzzy systems, clustering, naïve Bayes, and neural nets. The authors go on to cover methodologies used in time series and forecasting, such as ARIMA, GARCH, and survival analysis. They also present a range of optimization techniques and explore several special topics, such as Dempster–Shafer theory. An in-depth collection of the most important fundamental material on predictive analytics, this self-contained book provides the necessary information for understanding various techniques for exploratory data analysis and modeling. It explains the algorithmic details behind each technique (including underlying assumptions and mathematical formulations) and shows how to prepare and encode data, select variables, use model goodness measures, normalize odds, and perform reject inference. Web Resource The book’s website at www.DataMinerXL.com offers the DataMinerXL software for building predictive models. The site also includes more examples and information on modeling.
  closed form solution linear regression: Statistical Applications for Environmental Analysis and Risk Assessment Joseph Ofungwu, 2014-05-27 Statistical Applications for Environmental Analysis and Risk Assessment guides readers through real-world situations and the best statistical methods used to determine the nature and extent of the problem, evaluate the potential human health and ecological risks, and design and implement remedial systems as necessary. Featuring numerous worked examples using actual data and “ready-made” software scripts, Statistical Applications for Environmental Analysis and Risk Assessment also includes: • Descriptions of basic statistical concepts and principles in an informal style that does not presume prior familiarity with the subject • Detailed illustrations of statistical applications in the environmental and related water resources fields using real-world data in the contexts that would typically be encountered by practitioners • Software scripts using the high-powered statistical software system, R, and supplemented by USEPA’s ProUCL and USDOE’s VSP software packages, which are all freely available • Coverage of frequent data sample issues such as non-detects, outliers, skewness, sustained and cyclical trend that habitually plague environmental data samples • Clear demonstrations of the crucial, but often overlooked, role of statistics in environmental sampling design and subsequent exposure risk assessment.
  closed form solution linear regression: Machine Learning Andreas Lindholm, Niklas Wahlström, Fredrik Lindsten, Thomas B. Schön, 2022-03-31 Presents carefully selected supervised and unsupervised learning methods from basic to state-of-the-art,in a coherent statistical framework.
  closed form solution linear regression: Data Mining Methods and Models Daniel T. Larose, 2006-02-02 Apply powerful Data Mining Methods and Models to Leverage your Data for Actionable Results Data Mining Methods and Models provides: * The latest techniques for uncovering hidden nuggets of information * The insight into how the data mining algorithms actually work * The hands-on experience of performing data mining on large data sets Data Mining Methods and Models: * Applies a white box methodology, emphasizing an understanding of the model structures underlying the softwareWalks the reader through the various algorithms and provides examples of the operation of the algorithms on actual large data sets, including a detailed case study, Modeling Response to Direct-Mail Marketing * Tests the reader's level of understanding of the concepts and methodologies, with over 110 chapter exercises * Demonstrates the Clementine data mining software suite, WEKA open source data mining software, SPSS statistical software, and Minitab statistical software * Includes a companion Web site, www.dataminingconsultant.com, where the data sets used in the book may be downloaded, along with a comprehensive set of data mining resources. Faculty adopters of the book have access to an array of helpful resources, including solutions to all exercises, a PowerPoint(r) presentation of each chapter, sample data mining course projects and accompanying data sets, and multiple-choice chapter quizzes. With its emphasis on learning by doing, this is an excellent textbook for students in business, computer science, and statistics, as well as a problem-solving reference for data analysts and professionals in the field. An Instructor's Manual presenting detailed solutions to all the problems in the book is available onlne.
  closed form solution linear regression: Neural Networks: Tricks of the Trade Grégoire Montavon, Geneviève Orr, Klaus-Robert Müller, 2012-11-14 The twenty last years have been marked by an increase in available data and computing power. In parallel to this trend, the focus of neural network research and the practice of training neural networks has undergone a number of important changes, for example, use of deep learning machines. The second edition of the book augments the first edition with more tricks, which have resulted from 14 years of theory and experimentation by some of the world's most prominent neural network researchers. These tricks can make a substantial difference (in terms of speed, ease of implementation, and accuracy) when it comes to putting algorithms to work on real problems.
  closed form solution linear regression: Motion Vision J. Kolodko, L. Vlacic, 2005 This comprehensive book deals with motion estimation for autonomous systems from a biological, algorithmic and digital perspective. An algorithm, which is based on the optical flow constraint equation, is described in detail.
  closed form solution linear regression: The Mathematics of Machine Learning Maria Han Veiga, François Gaston Ged, 2024-05-20 This book is an introduction to machine learning, with a strong focus on the mathematics behind the standard algorithms and techniques in the field, aimed at senior undergraduates and early graduate students of Mathematics. There is a focus on well-known supervised machine learning algorithms, detailing the existing theory to provide some theoretical guarantees, featuring intuitive proofs and exposition of the material in a concise and precise manner. A broad set of topics is covered, giving an overview of the field. A summary of the topics covered is: statistical learning theory, approximation theory, linear models, kernel methods, Gaussian processes, deep neural networks, ensemble methods and unsupervised learning techniques, such as clustering and dimensionality reduction. This book is suited for students who are interested in entering the field, by preparing them to master the standard tools in Machine Learning. The reader will be equipped to understand the main theoretical questions of the current research and to engage with the field.
  closed form solution linear regression: Linear Factor Models in Finance John Knight, 2004-12-01 The determination of the values of stocks, bonds, options, futures, and derivatives is done by the scientific process of asset pricing, which has developed dramatically in the last few years due to advances in financial theory and econometrics. This book covers the science of asset pricing by concentrating on the most widely used modelling technique called: Linear Factor Modelling.Linear Factor Models covers an important area for Quantitative Analysts/Investment Managers who are developing Quantitative Investment Strategies. Linear factor models (LFM) are part of modern investment processes that include asset valuation, portfolio theory and applications, linear factor models and applications, dynamic asset allocation strategies, portfolio performance measurement, risk management, international perspectives, and the use of derivatives. The book develops the building blocks for one of the most important theories of asset pricing - Linear Factor Modelling. Within this framework, we can include other asset pricing theories such as the Capital Asset Pricing Model (CAPM), arbitrage pricing theory and various pricing formulae for derivatives and option prices. As a bare minimum, the reader of this book must have a working knowledge of basic calculus, simple optimisation and elementary statistics. In particular, the reader must be comfortable with the algebraic manipulation of means, variances (and covariances) of linear combination(s) of random variables. Some topics may require a greater mathematical sophistication.* Covers the latest methods in this area.* Combines actual quantitative finance experience with analytical research rigour* Written by both quantitative analysts and academics who work in this area
  closed form solution linear regression: Fundamentals of Design of Experiments for Automotive Engineering Volume I Young J. Chiang, Amy L. Chiang, 2023-11-28 In a world where innovation and sustainability are paramount, Fundamentals of Design of Experiments for Automotive Engineering: Volume I serves as a definitive guide to harnessing the power of statistical thinking in product development. As first of four volumes in SAE International’s DOE for Product Reliability Growth series, this book presents a practical, application-focused approach by emphasizing DOE as a dynamic tool for automotive engineers. It showcases real-world examples, demonstrating how process improvements and system optimizations can significantly enhance product reliability. The author, Yung Chiang, leverages extensive product development expertise to present a comprehensive process that ensures product performance and reliability throughout its entire lifecycle. Whether individuals are involved in research, design, testing, manufacturing, or marketing, this essential reference equips them with the skills needed to excel in their respective roles. This book explores the potential of Reliability and Sustainability with DOE, featuring the following topics: - Fundamental prerequisites for deploying DOE: Product reliability processes, measurement uncertainty, failure analysis, and design for reliability. - Full factorial design 2K: A system identification tool for relating objectives to factors and understanding main and interactive effects. - Fractional factorial design 2RK-P: Ideal for identifying main effects and 2-factor interactions. - General fractional factorial design LK-P: Systematically identification of significant inputs and analysis of nonlinear behaviors. - Composite designs as response surface methods: Resolving interactions and optimizing decisions with limited factors. - Adapting to practical challenges with “short” DOE: Leveraging optimization schemes like D-optimality, and A-optimality for optimal results. Readers are encouraged not to allow product failures to hinder progress but to embrace the statistical thinking embedded in DOE. This book can illuminate the path to designing products that stand the test of time, resulting in satisfied customers and thriving businesses. (ISBN 9781468606027, ISBN 9781468606034, ISBN 9781468606041, DOI 10.4271/9781468606034)
  closed form solution linear regression: Pro Deep Learning with TensorFlow Santanu Pattanayak, 2017-12-06 Deploy deep learning solutions in production with ease using TensorFlow. You'll also develop the mathematical understanding and intuition required to invent new deep learning architectures and solutions on your own. Pro Deep Learning with TensorFlow provides practical, hands-on expertise so you can learn deep learning from scratch and deploy meaningful deep learning solutions. This book will allow you to get up to speed quickly using TensorFlow and to optimize different deep learning architectures. All of the practical aspects of deep learning that are relevant in any industry are emphasized in this book. You will be able to use the prototypes demonstrated to build new deep learning applications. The code presented in the book is available in the form of iPython notebooks and scripts which allow you to try out examples and extend them in interesting ways. You will be equipped with the mathematical foundation and scientific knowledge to pursue research in this field and give back to the community. What You'll Learn Understand full stack deep learning using TensorFlow and gain a solid mathematical foundation for deep learning Deploy complex deep learning solutions in production using TensorFlow Carry out research on deep learning and perform experiments using TensorFlow Who This Book Is For Data scientists and machine learning professionals, software developers, graduate students, and open source enthusiasts
  closed form solution linear regression: Data Mining Charu C. Aggarwal, 2015-04-13 This textbook explores the different aspects of data mining from the fundamentals to the complex data types and their applications, capturing the wide diversity of problem domains for data mining issues. It goes beyond the traditional focus on data mining problems to introduce advanced data types such as text, time series, discrete sequences, spatial data, graph data, and social networks. Until now, no single book has addressed all these topics in a comprehensive and integrated way. The chapters of this book fall into one of three categories: Fundamental chapters: Data mining has four main problems, which correspond to clustering, classification, association pattern mining, and outlier analysis. These chapters comprehensively discuss a wide variety of methods for these problems. Domain chapters: These chapters discuss the specific methods used for different domains of data such as text data, time-series data, sequence data, graph data, and spatial data. Application chapters: These chapters study important applications such as stream mining, Web mining, ranking, recommendations, social networks, and privacy preservation. The domain chapters also have an applied flavor. Appropriate for both introductory and advanced data mining courses, Data Mining: The Textbook balances mathematical details and intuition. It contains the necessary mathematical details for professors and researchers, but it is presented in a simple and intuitive style to improve accessibility for students and industrial practitioners (including those with a limited mathematical background). Numerous illustrations, examples, and exercises are included, with an emphasis on semantically interpretable examples. Praise for Data Mining: The Textbook - “As I read through this book, I have already decided to use it in my classes. This is a book written by an outstanding researcher who has made fundamental contributions to data mining, in a way that is both accessible and up to date. The book is complete with theory and practical use cases. It’s a must-have for students and professors alike! -- Qiang Yang, Chair of Computer Science and Engineering at Hong Kong University of Science and Technology This is the most amazing and comprehensive text book on data mining. It covers not only the fundamental problems, such as clustering, classification, outliers and frequent patterns, and different data types, including text, time series, sequences, spatial data and graphs, but also various applications, such as recommenders, Web, social network and privacy. It is a great book for graduate students and researchers as well as practitioners. -- Philip S. Yu, UIC Distinguished Professor and Wexler Chair in Information Technology at University of Illinois at Chicago
  closed form solution linear regression: Learning Deep Learning Magnus Ekman, 2021-07-19 NVIDIA's Full-Color Guide to Deep Learning: All You Need to Get Started and Get Results To enable everyone to be part of this historic revolution requires the democratization of AI knowledge and resources. This book is timely and relevant towards accomplishing these lofty goals. -- From the foreword by Dr. Anima Anandkumar, Bren Professor, Caltech, and Director of ML Research, NVIDIA Ekman uses a learning technique that in our experience has proven pivotal to success—asking the reader to think about using DL techniques in practice. His straightforward approach is refreshing, and he permits the reader to dream, just a bit, about where DL may yet take us. -- From the foreword by Dr. Craig Clawson, Director, NVIDIA Deep Learning Institute Deep learning (DL) is a key component of today's exciting advances in machine learning and artificial intelligence. Learning Deep Learning is a complete guide to DL. Illuminating both the core concepts and the hands-on programming techniques needed to succeed, this book is ideal for developers, data scientists, analysts, and others--including those with no prior machine learning or statistics experience. After introducing the essential building blocks of deep neural networks, such as artificial neurons and fully connected, convolutional, and recurrent layers, Magnus Ekman shows how to use them to build advanced architectures, including the Transformer. He describes how these concepts are used to build modern networks for computer vision and natural language processing (NLP), including Mask R-CNN, GPT, and BERT. And he explains how a natural language translator and a system generating natural language descriptions of images. Throughout, Ekman provides concise, well-annotated code examples using TensorFlow with Keras. Corresponding PyTorch examples are provided online, and the book thereby covers the two dominating Python libraries for DL used in industry and academia. He concludes with an introduction to neural architecture search (NAS), exploring important ethical issues and providing resources for further learning. Explore and master core concepts: perceptrons, gradient-based learning, sigmoid neurons, and back propagation See how DL frameworks make it easier to develop more complicated and useful neural networks Discover how convolutional neural networks (CNNs) revolutionize image classification and analysis Apply recurrent neural networks (RNNs) and long short-term memory (LSTM) to text and other variable-length sequences Master NLP with sequence-to-sequence networks and the Transformer architecture Build applications for natural language translation and image captioning NVIDIA's invention of the GPU sparked the PC gaming market. The company's pioneering work in accelerated computing--a supercharged form of computing at the intersection of computer graphics, high-performance computing, and AI--is reshaping trillion-dollar industries, such as transportation, healthcare, and manufacturing, and fueling the growth of many others. Register your book for convenient access to downloads, updates, and/or corrections as they become available. See inside book for details.
  closed form solution linear regression: Computer Vision – ACCV 2016 Shang-Hong Lai, Vincent Lepetit, Ko Nishino, Yoichi Sato, 2017-03-09 The five-volume set LNCS 10111-10115 constitutes the thoroughly refereed post-conference proceedings of the 13th Asian Conference on Computer Vision, ACCV 2016, held in Taipei, Taiwan, in November 2016. The total of 143 contributions presented in these volumes was carefully reviewed and selected from 479 submissions. The papers are organized in topical sections on Segmentation and Classification; Segmentation and Semantic Segmentation; Dictionary Learning, Retrieval, and Clustering; Deep Learning; People Tracking and Action Recognition; People and Actions; Faces; Computational Photography; Face and Gestures; Image Alignment; Computational Photography and Image Processing; Language and Video; 3D Computer Vision; Image Attributes, Language, and Recognition; Video Understanding; and 3D Vision.
  closed form solution linear regression: Applied Statistics for the Social and Health Sciences Rachel A. Gordon, 2023-11-15 For graduate students in the social and health sciences, featuring essential concepts and equations most often needed in scholarly publications. Uses excerpts from the scholarly literature in these fields to introduce new concepts. Uses publicly-available data that are regularly used in social and health science publications to introduce Stata code and illustrate concepts and interpretation. Thoroughly integrates the teaching of statistical theory with teaching data processing and analysis. Offers guidance about planning projects and organizing code for reproducibility Shows how to recognize critiques of the constructions, terminology, and interpretations of statistics. New edition focuses on Stata, with code integrated into the chapters (rather than appendices, as in the first edition) includes Stata’s factor variables and margins commands and Long and Freese’s (2014) spost13 commands, to simplify programming and facilitate interpretation.
  closed form solution linear regression: Machine Learners Adrian Mackenzie, 2017-11-16 If machine learning transforms the nature of knowledge, does it also transform the practice of critical thought? Machine learning—programming computers to learn from data—has spread across scientific disciplines, media, entertainment, and government. Medical research, autonomous vehicles, credit transaction processing, computer gaming, recommendation systems, finance, surveillance, and robotics use machine learning. Machine learning devices (sometimes understood as scientific models, sometimes as operational algorithms) anchor the field of data science. They have also become mundane mechanisms deeply embedded in a variety of systems and gadgets. In contexts from the everyday to the esoteric, machine learning is said to transform the nature of knowledge. In this book, Adrian Mackenzie investigates whether machine learning also transforms the practice of critical thinking. Mackenzie focuses on machine learners—either humans and machines or human-machine relations—situated among settings, data, and devices. The settings range from fMRI to Facebook; the data anything from cat images to DNA sequences; the devices include neural networks, support vector machines, and decision trees. He examines specific learning algorithms—writing code and writing about code—and develops an archaeology of operations that, following Foucault, views machine learning as a form of knowledge production and a strategy of power. Exploring layers of abstraction, data infrastructures, coding practices, diagrams, mathematical formalisms, and the social organization of machine learning, Mackenzie traces the mostly invisible architecture of one of the central zones of contemporary technological cultures. Mackenzie's account of machine learning locates places in which a sense of agency can take root. His archaeology of the operational formation of machine learning does not unearth the footprint of a strategic monolith but reveals the local tributaries of force that feed into the generalization and plurality of the field.
  closed form solution linear regression: Statistical Computing Kennedy, 1980-03-01 This book provides an introduction to statistical computing and a critical, balanced presentation of the algorithms and computational methods used in software systems, discussing techniques for implementing algorithms in a computer. It is intended for graduate students in statistics.
  closed form solution linear regression: Iterative Methods for Sparse Linear Systems Yousef Saad, 2003-04-01 Mathematics of Computing -- General.
  closed form solution linear regression: Advances in Information Retrieval Mohand Boughanem, Catherine Berrut, Josiane Mothe, Chantal Soule-Dupuy, 2009-03-27 This book constitutes the refereed proceedings of the 30th annual European Conference on Information Retrieval Research, ECIR 2009, held in Toulouse, France in April 2009. The 42 revised full papers and 18 revised short papers presented together with the abstracts of 3 invited lectures and 25 poster papers were carefully reviewed and selected from 188 submissions. The papers are organized in topical sections on retrieval model, collaborative IR / filtering, learning, multimedia - metadata, expert search - advertising, evaluation, opinion detection, web IR, representation, clustering / categorization as well as distributed IR.
  closed form solution linear regression: Artificial Intelligence Charu C. Aggarwal, 2021-07-16 This textbook covers the broader field of artificial intelligence. The chapters for this textbook span within three categories: Deductive reasoning methods: These methods start with pre-defined hypotheses and reason with them in order to arrive at logically sound conclusions. The underlying methods include search and logic-based methods. These methods are discussed in Chapters 1through 5. Inductive Learning Methods: These methods start with examples and use statistical methods in order to arrive at hypotheses. Examples include regression modeling, support vector machines, neural networks, reinforcement learning, unsupervised learning, and probabilistic graphical models. These methods are discussed in Chapters~6 through 11. Integrating Reasoning and Learning: Chapters~11 and 12 discuss techniques for integrating reasoning and learning. Examples include the use of knowledge graphs and neuro-symbolic artificial intelligence. The primary audience for this textbook are professors and advanced-level students in computer science. It is also possible to use this textbook for the mathematics requirements for an undergraduate data science course. Professionals working in this related field many also find this textbook useful as a reference.
  closed form solution linear regression: Machine Learning Algorithms Fuwei Li, Lifeng Lai, Shuguang Cui, 2022-11-14 This book demonstrates the optimal adversarial attacks against several important signal processing algorithms. Through presenting the optimal attacks in wireless sensor networks, array signal processing, principal component analysis, etc, the authors reveal the robustness of the signal processing algorithms against adversarial attacks. Since data quality is crucial in signal processing, the adversary that can poison the data will be a significant threat to signal processing. Therefore, it is necessary and urgent to investigate the behavior of machine learning algorithms in signal processing under adversarial attacks. The authors in this book mainly examine the adversarial robustness of three commonly used machine learning algorithms in signal processing respectively: linear regression, LASSO-based feature selection, and principal component analysis (PCA). As to linear regression, the authors derive the optimal poisoning data sample and the optimal feature modifications, and also demonstrate the effectiveness of the attack against a wireless distributed learning system. The authors further extend the linear regression to LASSO-based feature selection and study the best strategy to mislead the learning system to select the wrong features. The authors find the optimal attack strategy by solving a bi-level optimization problem and also illustrate how this attack influences array signal processing and weather data analysis. In the end, the authors consider the adversarial robustness of the subspace learning problem. The authors examine the optimal modification strategy under the energy constraints to delude the PCA-based subspace learning algorithm. This book targets researchers working in machine learning, electronic information, and information theory as well as advanced-level students studying these subjects. R&D engineers who are working in machine learning, adversarial machine learning, robust machine learning, and technical consultants working on the security and robustness of machine learning are likely to purchase this book as a reference guide.
  closed form solution linear regression: ECAI 2010 European Coordinating Committee for Artificial Intelligence, 2010 LC copy bound in 2 v.: v. 1, p. 1-509; v. 2, p. [509]-1153.
  closed form solution linear regression: Robotics Research Antonio Bicchi, Wolfram Burgard, 2017-07-25 ISRR, the International Symposium on Robotics Research, is one of robotics pioneering Symposia, which has established over the past two decades some of the field's most fundamental and lasting contributions. This book presents the results of the seventeenth edition of Robotics Research ISRR15, offering a collection of a broad range of topics in robotics. The content of the contributions provides a wide coverage of the current state of robotics research.: the advances and challenges in its theoretical foundation and technology basis, and the developments in its traditional and new emerging areas of applications. The diversity, novelty, and span of the work unfolding in these areas reveal the field's increased maturity and expanded scope and define the state of the art of robotics and its future direction.
  closed form solution linear regression: Unconventional Methods for Geoscience, Shale Gas and Petroleum in the 21st Century J. Watada, S.C. Tan, P.-C. Lin, 2023-09-11 Since the turn of the century, geology has advanced dramatically, with materials derived from extra-terrestrial sources meaning that it now encompasses cosmology, and new technologies providing ever more sophisticated possibilities for the conducting of research. This book, Unconventional Methods for Geoscience, Shale Gas and Petroleum in the 21st Century, aims to provide research directions for geology in the 21st century. As Eric Hobsbawm wrote, it is difficult to write the history of one’s own days, and selecting influential methods was no easy task, but an attempt has been made to include the most influential papers that represent the smart geology of the first few decades of the 21st century. The book presents 22 papers; the first serves as an introduction to biology, which is now expanding into the science of the cosmos following the discovery of previously missing information, and the remaining 21 papers are divided into 3 sections entitled Modelling, Simulation and Optimization. The importance of theoretical approaches from physics, mathematics, and statistics underlying meta-heuristic methods, knowledge and approaches is acknowledged, and there is a chapter dedicated to deep learning. The book contributes to the exploration of various possible solutions to challenging problems in both the Earth’s geology and that of the cosmos, and will be of interest to all those working in the field.

  closed-form solution linear regression: Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow Aurélien Géron, 2019-09-05 Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. Now, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how. By using concrete examples, minimal theory, and two production-ready Python frameworks—Scikit-Learn and TensorFlow—author Aurélien Géron helps you gain an intuitive understanding of the concepts and tools for building intelligent systems. You’ll learn a range of techniques, starting with simple linear regression and progressing to deep neural networks. With exercises in each chapter to help you apply what you’ve learned, all you need is programming experience to get started. Explore the machine learning landscape, particularly neural nets Use Scikit-Learn to track an example machine-learning project end-to-end Explore several training models, including support vector machines, decision trees, random forests, and ensemble methods Use the TensorFlow library to build and train neural nets Dive into neural net architectures, including convolutional nets, recurrent nets, and deep reinforcement learning Learn techniques for training and scaling deep neural nets
  closed-form solution linear regression: Probability and Statistics for Machine Learning Charu C. Aggarwal,
  closed-form solution linear regression: Machine Learning Fundamentals Hui Jiang, 2021-11-25 A coherent introduction to core concepts and deep learning techniques that are critical to academic research and real-world applications.
  closed-form solution linear regression: An Introduction to Machine Learning Gopinath Rebala, Ajay Ravi, Sanjay Churiwala, 2019-05-07 Just like electricity, Machine Learning will revolutionize our life in many ways – some of which are not even conceivable today. This book provides a thorough conceptual understanding of Machine Learning techniques and algorithms. Many of the mathematical concepts are explained in an intuitive manner. The book starts with an overview of machine learning and the underlying Mathematical and Statistical concepts before moving onto machine learning topics. It gradually builds up the depth, covering many of the present day machine learning algorithms, ending in Deep Learning and Reinforcement Learning algorithms. The book also covers some of the popular Machine Learning applications. The material in this book is agnostic to any specific programming language or hardware so that readers can try these concepts on whichever platforms they are already familiar with. Offers a comprehensive introduction to Machine Learning, while not assuming any prior knowledge of the topic; Provides a complete overview of available techniques and algorithms in conceptual terms, covering various application domains of machine learning; Not tied to any specific software language or hardware implementation.
  closed-form solution linear regression: Materials Data Science Stefan Sandfeld,
  closed-form solution linear regression: Kernel Methods in Computer Vision Christoph H. Lampert, 2009 Few developments have influenced the field of computer vision in the last decade more than the introduction of statistical machine learning techniques. Particularly kernel-based classifiers, such as the support vector machine, have become indispensable tools, providing a unified framework for solving a wide range of image-related prediction tasks, including face recognition, object detection and action classification. By emphasizing the geometric intuition that all kernel methods rely on, Kernel Methods in Computer Vision provides an introduction to kernel-based machine learning techniques accessible to a wide audience including students, researchers and practitioners alike, without sacrificing mathematical correctness. It covers not only support vector machines but also less known techniques for kernel-based regression, outlier detection, clustering and dimensionality reduction. Additionally, it offers an outlook on recent developments in kernel methods that have not yet made it into the regular textbooks: structured prediction, dependency estimation and learning of the kernel function. Each topic is illustrated with examples of successful application in the computer vision literature, making Kernel Methods in Computer Vision a useful guide not only for those wanting to understand the working principles of kernel methods, but also for anyone wanting to apply them to real-life problems.
  closed-form solution linear regression: Hands-On Machine Learning with Scikit-Learn and TensorFlow Aurélien Géron, 2017-03-13 Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. Now, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how. By using concrete examples, minimal theory, and two production-ready Python frameworks--scikit-learn and TensorFlow--author Aurélien Géron helps you gain an intuitive understanding of the concepts and tools for building intelligent systems. You'll learn a range of techniques, starting with simple linear regression and progressing to deep neural networks. With exercises in each chapter to help you apply what you've learned, all you need is programming experience to get started.
  closed-form solution linear regression: Econometric Methods with Applications in Business and Economics Christiaan Heij, Paul de Boer, Philip Hans Franses, Teun Kloek, Herman K. van Dijk, All at the Erasmus University in Rotterdam, 2004-03-25 Nowadays applied work in business and economics requires a solid understanding of econometric methods to support decision-making. Combining a solid exposition of econometric methods with an application-oriented approach, this rigorous textbook provides students with a working understanding and hands-on experience of current econometrics. Taking a 'learning by doing' approach, it covers basic econometric methods (statistics, simple and multiple regression, nonlinear regression, maximum likelihood, and generalized method of moments), and addresses the creative process of model building with due attention to diagnostic testing and model improvement. Its last part is devoted to two major application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and the econometrics of time series data (univariate time series, trends, volatility, vector autoregressions, and a brief discussion of SUR models, panel data, and simultaneous equations). · Real-world text examples and practical exercise questions stimulate active learning and show how econometrics can solve practical questions in modern business and economic management. · Focuses on the core of econometrics, regression, and covers two major advanced topics, choice data with applications in marketing and micro-economics, and time series data with applications in finance and macro-economics. · Learning-support features include concise, manageable sections of text, frequent cross-references to related and background material, summaries, computational schemes, keyword lists, suggested further reading, exercise sets, and online data sets and solutions. · Derivations and theory exercises are clearly marked for students in advanced courses. This textbook is perfect for advanced undergraduate students, new graduate students, and applied researchers in econometrics, business, and economics, and for researchers in other fields that draw on modern applied econometrics.
  closed-form solution linear regression: Multi-way Analysis Age Smilde, Rasmus Bro, Paul Geladi, 2005-06-10 This book is an introduction to the field of multi-way analysis for chemists and chemometricians. Its emphasis is on the ideas behind the method and its pratical applications. Sufficient mathematical background is given to provide a solid understanding of the ideas behind the method. There are currently no other books on the market which deal with this method from the viewpoint of its applications in chemistry. Applicable in many areas of chemistry. No comparable volume currently available. The field is becoming increasingly important.
  closed-form solution linear regression: Classification and Knowledge Organization Rüdiger Klar, Otto Opitz, 2013-03-14 Large collections of data and information necessitate adequate methods for their analysis. The book presents such methods, proposes and discusses recent approaches and implementations and describes a series of practical applications.
  closed-form solution linear regression: Predictions, Nonlinearities and Portfolio Choice Friedrich Christian Kruse, 2012 Finance researchers and asset management practitioners put a lot of effort into the question of optimal asset allocation. With this respect, a lot of research has been conducted on portfolio decision making as well as quantitative modeling and prediction models. This study brings together three fields of research, which are usually analyzed in an isolated manner in the literature: - Predictability of asset returns and their covariance matrix - Optimal portfolio decision making - Nonlinear modeling, performed by artificial neural networks, and their impact on predictions as well as optimal portfolio construction Including predictability in asset allocation is the focus of this work and it pays special attention to issues related to nonlinearities. The contribution of this study to the portfolio choice literature is twofold. First, motivated by the evidence of linear predictability, the impact of nonlinear predictions on portfolio performances is analyzed. Predictions are empirically performed for an investor who invests in equities (represented by the DAX index), bonds (represented by the REXP index) and a risk-free rate. Second, a solution to the dynamic programming problem for intertemporal portfolio choice is presented. The method is based on functional approximations of the investor's value function with artificial neural networks. The method is easily capable of handling multiple state variables. Hence, the effect of adding predictive parameters to the state space is the focus of analysis as well as the impacts of estimation biases and the view of a Bayesian investor on intertemporal portfolio choice. One important empirical result shows that residual correlation among state variables have an impact on intertemporal portfolio decision making.
  closed-form solution linear regression: Linear Algebra and Optimization for Machine Learning Charu C. Aggarwal, 2020-05-13 This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout the book. A solution manual for the exercises at the end of each chapter is available to teaching instructors. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows: 1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts. 2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning.
  closed-form solution linear regression: Clinical Trial Data Analysis Using R Ding-Geng (Din) Chen, Karl E. Peace, 2010-12-14 Too often in biostatistical research and clinical trials, a knowledge gap exists between developed statistical methods and the applications of these methods. Filling this gap, Clinical Trial Data Analysis Using R provides a thorough presentation of biostatistical analyses of clinical trial data and shows step by step how to implement the statistical methods using R. The book’s practical, detailed approach draws on the authors’ 30 years of real-world experience in biostatistical research and clinical development. Each chapter presents examples of clinical trials based on the authors’ actual experiences in clinical drug development. Various biostatistical methods for analyzing the data are then identified. The authors develop analysis code step by step using appropriate R packages and functions. This approach enables readers to gain an understanding of the analysis methods and R implementation so that they can use R to analyze their own clinical trial data. With step-by-step illustrations of R implementations, this book shows how to easily use R to simulate and analyze data from a clinical trial. It describes numerous up-to-date statistical methods and offers sound guidance on the processes involved in clinical trials.
  closed-form solution linear regression: Case Studies in Bayesian Statistical Modelling and Analysis Clair L. Alston, Kerrie L. Mengersen, Anthony N. Pettitt, 2012-10-10 Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing. Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.
  closed-form solution linear regression: Intelligent Computing: An Introduction to Artificial Intelligence Book Dr. Shivamurthaiah M , Dr. Praveen Kumar K, Dr. Vinay S, Prof. Rakesh Podaralla, 2023-10-20 In this book named ‘Intelligent Computing: An Introduction to Artificial Intelligence.’ the authors try to give detailed information on various aspects of Intelligent computing. This book consists of seven chapters from Introduction to AI to the Future of AI. The first chapter consists of the Introduction, history importance, and impact of intelligent computing in various fields. The Second chapter gives information about the Foundations of Artificial Intelligence which is cognitive science and its relation to AI. It also explains the Key concepts of Machine learning, Neural networks, Natural language processing and followed by concepts of Robotics. The third chapter explains Intelligent Computing Techniques named Supervised learning: Linear regression, Logistic regression, Support vector machines, Unsupervised learning: Clustering algorithms, Dimensionality reduction, Association rule mining, Deep learning: Neural network architectures, Convolutional neural networks, Recurrent neural networks: Generative adversarial networks, Reinforcement learning, Markov decision processes, Q-learning, Deep reinforcement learning. The fourth chapter consists of information about Applications of Intelligent Computing. Natural language processing applications: Sentiment analysis, Speech recognition, Machine translation, Computer vision applications like Object detection and recognition, Image classification, Facial recognition, Robotics applications Like Autonomous Vehicles, Industrial Automation, human robots, Healthcare applications, Disease diagnosis, Medical Image Analysis & Drug discovery. The fifth chapter consists of topics on the Ethical and Social prospective of the Implications of Intelligent Computing covers the Limitations & strengths of AI algorithms, Privacy and security concerns, Automation and its impact on job displacement also about governance and regulations on AI by the government. The sixth Chapter contains Future Directions and Challenges in Intelligent Computing Advances like interpretability of AI systems, Human-AI collaboration and augmentation, and Addressing ethical and societal challenges. The last chapter gives a conclusion about the topic: key points of AI, its Potential impact in the future & required Encouragement for further exploration of AI and intelligent computing. This book gives detailed enough information for the reader to enhance their knowledge of Intelligent Computing and AI.
  closed-form solution linear regression: Computational Intelligence in Data Mining - Volume 2 Lakhmi C. Jain, Himansu Sekhar Behera, Jyotsna Kumar Mandal, Durga Prasad Mohapatra, 2014-12-10 The contributed volume aims to explicate and address the difficulties and challenges that of seamless integration of the two core disciplines of computer science, i.e., computational intelligence and data mining. Data Mining aims at the automatic discovery of underlying non-trivial knowledge from datasets by applying intelligent analysis techniques. The interest in this research area has experienced a considerable growth in the last years due to two key factors: (a) knowledge hidden in organizations’ databases can be exploited to improve strategic and managerial decision-making; (b) the large volume of data managed by organizations makes it impossible to carry out a manual analysis. The book addresses different methods and techniques of integration for enhancing the overall goal of data mining. The book helps to disseminate the knowledge about some innovative, active research directions in the field of data mining, machine and computational intelligence, along with some current issues and applications of related topics.
  closed-form solution linear regression: Large-Scale Data Analytics with Python and Spark Isaac Triguero, Mikel Galar, 2023-11-23 Based on the authors' extensive teaching experience, this hands-on graduate-level textbook teaches how to carry out large-scale data analytics and design machine learning solutions for big data. With a focus on fundamentals, this extensively class-tested textbook walks students through key principles and paradigms for working with large-scale data, frameworks for large-scale data analytics (Hadoop, Spark), and explains how to implement machine learning to exploit big data. It is unique in covering the principles that aspiring data scientists need to know, without detail that can overwhelm. Real-world examples, hands-on coding exercises and labs combine with exceptionally clear explanations to maximize student engagement. Well-defined learning objectives, exercises with online solutions for instructors, lecture slides, and an accompanying suite of lab exercises of increasing difficulty in Jupyter Notebooks offer a coherent and convenient teaching package. An ideal teaching resource for courses on large-scale data analytics with machine learning in computer/data science departments.
  closed-form solution linear regression: Foundations of Predictive Analytics James Wu, Stephen Coggeshall, 2012-02-15 Drawing on the authors’ two decades of experience in applied modeling and data mining, Foundations of Predictive Analytics presents the fundamental background required for analyzing data and building models for many practical applications, such as consumer behavior modeling, risk and marketing analytics, and other areas. It also discusses a variety of practical topics that are frequently missing from similar texts. The book begins with the statistical and linear algebra/matrix foundation of modeling methods, from distributions to cumulant and copula functions to Cornish–Fisher expansion and other useful but hard-to-find statistical techniques. It then describes common and unusual linear methods as well as popular nonlinear modeling approaches, including additive models, trees, support vector machine, fuzzy systems, clustering, naïve Bayes, and neural nets. The authors go on to cover methodologies used in time series and forecasting, such as ARIMA, GARCH, and survival analysis. They also present a range of optimization techniques and explore several special topics, such as Dempster–Shafer theory. An in-depth collection of the most important fundamental material on predictive analytics, this self-contained book provides the necessary information for understanding various techniques for exploratory data analysis and modeling. It explains the algorithmic details behind each technique (including underlying assumptions and mathematical formulations) and shows how to prepare and encode data, select variables, use model goodness measures, normalize odds, and perform reject inference. Web Resource The book’s website at www.DataMinerXL.com offers the DataMinerXL software for building predictive models. The site also includes more examples and information on modeling.
  closed-form solution linear regression: Statistical Applications for Environmental Analysis and Risk Assessment Joseph Ofungwu, 2014-05-27 Statistical Applications for Environmental Analysis and Risk Assessment guides readers through real-world situations and the best statistical methods used to determine the nature and extent of the problem, evaluate the potential human health and ecological risks, and design and implement remedial systems as necessary. Featuring numerous worked examples using actual data and “ready-made” software scripts, Statistical Applications for Environmental Analysis and Risk Assessment also includes: • Descriptions of basic statistical concepts and principles in an informal style that does not presume prior familiarity with the subject • Detailed illustrations of statistical applications in the environmental and related water resources fields using real-world data in the contexts that would typically be encountered by practitioners • Software scripts using the high-powered statistical software system, R, and supplemented by USEPA’s ProUCL and USDOE’s VSP software packages, which are all freely available • Coverage of frequent data sample issues such as non-detects, outliers, skewness, sustained and cyclical trend that habitually plague environmental data samples • Clear demonstrations of the crucial, but often overlooked, role of statistics in environmental sampling design and subsequent exposure risk assessment.
  closed-form solution linear regression: Machine Learning Andreas Lindholm, Niklas Wahlström, Fredrik Lindsten, Thomas B. Schön, 2022-03-31 Presents carefully selected supervised and unsupervised learning methods from basic to state-of-the-art,in a coherent statistical framework.
  closed-form solution linear regression: Data Mining Methods and Models Daniel T. Larose, 2006-02-02 Apply powerful Data Mining Methods and Models to Leverage your Data for Actionable Results Data Mining Methods and Models provides: * The latest techniques for uncovering hidden nuggets of information * The insight into how the data mining algorithms actually work * The hands-on experience of performing data mining on large data sets Data Mining Methods and Models: * Applies a white box methodology, emphasizing an understanding of the model structures underlying the softwareWalks the reader through the various algorithms and provides examples of the operation of the algorithms on actual large data sets, including a detailed case study, Modeling Response to Direct-Mail Marketing * Tests the reader's level of understanding of the concepts and methodologies, with over 110 chapter exercises * Demonstrates the Clementine data mining software suite, WEKA open source data mining software, SPSS statistical software, and Minitab statistical software * Includes a companion Web site, www.dataminingconsultant.com, where the data sets used in the book may be downloaded, along with a comprehensive set of data mining resources. Faculty adopters of the book have access to an array of helpful resources, including solutions to all exercises, a PowerPoint(r) presentation of each chapter, sample data mining course projects and accompanying data sets, and multiple-choice chapter quizzes. With its emphasis on learning by doing, this is an excellent textbook for students in business, computer science, and statistics, as well as a problem-solving reference for data analysts and professionals in the field. An Instructor's Manual presenting detailed solutions to all the problems in the book is available onlne.
  closed-form solution linear regression: Neural Networks: Tricks of the Trade Grégoire Montavon, Geneviève Orr, Klaus-Robert Müller, 2012-11-14 The twenty last years have been marked by an increase in available data and computing power. In parallel to this trend, the focus of neural network research and the practice of training neural networks has undergone a number of important changes, for example, use of deep learning machines. The second edition of the book augments the first edition with more tricks, which have resulted from 14 years of theory and experimentation by some of the world's most prominent neural network researchers. These tricks can make a substantial difference (in terms of speed, ease of implementation, and accuracy) when it comes to putting algorithms to work on real problems.
  closed-form solution linear regression: Motion Vision J. Kolodko, L. Vlacic, 2005 This comprehensive book deals with motion estimation for autonomous systems from a biological, algorithmic and digital perspective. An algorithm, which is based on the optical flow constraint equation, is described in detail.
  closed-form solution linear regression: The Mathematics of Machine Learning Maria Han Veiga, François Gaston Ged, 2024-05-20 This book is an introduction to machine learning, with a strong focus on the mathematics behind the standard algorithms and techniques in the field, aimed at senior undergraduates and early graduate students of Mathematics. There is a focus on well-known supervised machine learning algorithms, detailing the existing theory to provide some theoretical guarantees, featuring intuitive proofs and exposition of the material in a concise and precise manner. A broad set of topics is covered, giving an overview of the field. A summary of the topics covered is: statistical learning theory, approximation theory, linear models, kernel methods, Gaussian processes, deep neural networks, ensemble methods and unsupervised learning techniques, such as clustering and dimensionality reduction. This book is suited for students who are interested in entering the field, by preparing them to master the standard tools in Machine Learning. The reader will be equipped to understand the main theoretical questions of the current research and to engage with the field.
  closed-form solution linear regression: Linear Factor Models in Finance John Knight, 2004-12-01 The determination of the values of stocks, bonds, options, futures, and derivatives is done by the scientific process of asset pricing, which has developed dramatically in the last few years due to advances in financial theory and econometrics. This book covers the science of asset pricing by concentrating on the most widely used modelling technique called: Linear Factor Modelling.Linear Factor Models covers an important area for Quantitative Analysts/Investment Managers who are developing Quantitative Investment Strategies. Linear factor models (LFM) are part of modern investment processes that include asset valuation, portfolio theory and applications, linear factor models and applications, dynamic asset allocation strategies, portfolio performance measurement, risk management, international perspectives, and the use of derivatives. The book develops the building blocks for one of the most important theories of asset pricing - Linear Factor Modelling. Within this framework, we can include other asset pricing theories such as the Capital Asset Pricing Model (CAPM), arbitrage pricing theory and various pricing formulae for derivatives and option prices. As a bare minimum, the reader of this book must have a working knowledge of basic calculus, simple optimisation and elementary statistics. In particular, the reader must be comfortable with the algebraic manipulation of means, variances (and covariances) of linear combination(s) of random variables. Some topics may require a greater mathematical sophistication.* Covers the latest methods in this area.* Combines actual quantitative finance experience with analytical research rigour* Written by both quantitative analysts and academics who work in this area
  closed-form solution linear regression: Fundamentals of Design of Experiments for Automotive Engineering Volume I Young J. Chiang, Amy L. Chiang, 2023-11-28 In a world where innovation and sustainability are paramount, Fundamentals of Design of Experiments for Automotive Engineering: Volume I serves as a definitive guide to harnessing the power of statistical thinking in product development. As first of four volumes in SAE International’s DOE for Product Reliability Growth series, this book presents a practical, application-focused approach by emphasizing DOE as a dynamic tool for automotive engineers. It showcases real-world examples, demonstrating how process improvements and system optimizations can significantly enhance product reliability. The author, Yung Chiang, leverages extensive product development expertise to present a comprehensive process that ensures product performance and reliability throughout its entire lifecycle. Whether individuals are involved in research, design, testing, manufacturing, or marketing, this essential reference equips them with the skills needed to excel in their respective roles. This book explores the potential of Reliability and Sustainability with DOE, featuring the following topics: - Fundamental prerequisites for deploying DOE: Product reliability processes, measurement uncertainty, failure analysis, and design for reliability. - Full factorial design 2K: A system identification tool for relating objectives to factors and understanding main and interactive effects. - Fractional factorial design 2RK-P: Ideal for identifying main effects and 2-factor interactions. - General fractional factorial design LK-P: Systematically identification of significant inputs and analysis of nonlinear behaviors. - Composite designs as response surface methods: Resolving interactions and optimizing decisions with limited factors. - Adapting to practical challenges with “short” DOE: Leveraging optimization schemes like D-optimality, and A-optimality for optimal results. Readers are encouraged not to allow product failures to hinder progress but to embrace the statistical thinking embedded in DOE. This book can illuminate the path to designing products that stand the test of time, resulting in satisfied customers and thriving businesses. (ISBN 9781468606027, ISBN 9781468606034, ISBN 9781468606041, DOI 10.4271/9781468606034)
  closed-form solution linear regression: Pro Deep Learning with TensorFlow Santanu Pattanayak, 2017-12-06 Deploy deep learning solutions in production with ease using TensorFlow. You'll also develop the mathematical understanding and intuition required to invent new deep learning architectures and solutions on your own. Pro Deep Learning with TensorFlow provides practical, hands-on expertise so you can learn deep learning from scratch and deploy meaningful deep learning solutions. This book will allow you to get up to speed quickly using TensorFlow and to optimize different deep learning architectures. All of the practical aspects of deep learning that are relevant in any industry are emphasized in this book. You will be able to use the prototypes demonstrated to build new deep learning applications. The code presented in the book is available in the form of iPython notebooks and scripts which allow you to try out examples and extend them in interesting ways. You will be equipped with the mathematical foundation and scientific knowledge to pursue research in this field and give back to the community. What You'll Learn Understand full stack deep learning using TensorFlow and gain a solid mathematical foundation for deep learning Deploy complex deep learning solutions in production using TensorFlow Carry out research on deep learning and perform experiments using TensorFlow Who This Book Is For Data scientists and machine learning professionals, software developers, graduate students, and open source enthusiasts
  closed-form solution linear regression: Data Mining Charu C. Aggarwal, 2015-04-13 This textbook explores the different aspects of data mining from the fundamentals to the complex data types and their applications, capturing the wide diversity of problem domains for data mining issues. It goes beyond the traditional focus on data mining problems to introduce advanced data types such as text, time series, discrete sequences, spatial data, graph data, and social networks. Until now, no single book has addressed all these topics in a comprehensive and integrated way. The chapters of this book fall into one of three categories: Fundamental chapters: Data mining has four main problems, which correspond to clustering, classification, association pattern mining, and outlier analysis. These chapters comprehensively discuss a wide variety of methods for these problems. Domain chapters: These chapters discuss the specific methods used for different domains of data such as text data, time-series data, sequence data, graph data, and spatial data. Application chapters: These chapters study important applications such as stream mining, Web mining, ranking, recommendations, social networks, and privacy preservation. The domain chapters also have an applied flavor. Appropriate for both introductory and advanced data mining courses, Data Mining: The Textbook balances mathematical details and intuition. It contains the necessary mathematical details for professors and researchers, but it is presented in a simple and intuitive style to improve accessibility for students and industrial practitioners (including those with a limited mathematical background). Numerous illustrations, examples, and exercises are included, with an emphasis on semantically interpretable examples. Praise for Data Mining: The Textbook - “As I read through this book, I have already decided to use it in my classes. This is a book written by an outstanding researcher who has made fundamental contributions to data mining, in a way that is both accessible and up to date. The book is complete with theory and practical use cases. It’s a must-have for students and professors alike! -- Qiang Yang, Chair of Computer Science and Engineering at Hong Kong University of Science and Technology This is the most amazing and comprehensive text book on data mining. It covers not only the fundamental problems, such as clustering, classification, outliers and frequent patterns, and different data types, including text, time series, sequences, spatial data and graphs, but also various applications, such as recommenders, Web, social network and privacy. It is a great book for graduate students and researchers as well as practitioners. -- Philip S. Yu, UIC Distinguished Professor and Wexler Chair in Information Technology at University of Illinois at Chicago
  closed-form solution linear regression: Learning Deep Learning Magnus Ekman, 2021-07-19 NVIDIA's Full-Color Guide to Deep Learning: All You Need to Get Started and Get Results To enable everyone to be part of this historic revolution requires the democratization of AI knowledge and resources. This book is timely and relevant towards accomplishing these lofty goals. -- From the foreword by Dr. Anima Anandkumar, Bren Professor, Caltech, and Director of ML Research, NVIDIA Ekman uses a learning technique that in our experience has proven pivotal to success—asking the reader to think about using DL techniques in practice. His straightforward approach is refreshing, and he permits the reader to dream, just a bit, about where DL may yet take us. -- From the foreword by Dr. Craig Clawson, Director, NVIDIA Deep Learning Institute Deep learning (DL) is a key component of today's exciting advances in machine learning and artificial intelligence. Learning Deep Learning is a complete guide to DL. Illuminating both the core concepts and the hands-on programming techniques needed to succeed, this book is ideal for developers, data scientists, analysts, and others--including those with no prior machine learning or statistics experience. After introducing the essential building blocks of deep neural networks, such as artificial neurons and fully connected, convolutional, and recurrent layers, Magnus Ekman shows how to use them to build advanced architectures, including the Transformer. He describes how these concepts are used to build modern networks for computer vision and natural language processing (NLP), including Mask R-CNN, GPT, and BERT. And he explains how a natural language translator and a system generating natural language descriptions of images. Throughout, Ekman provides concise, well-annotated code examples using TensorFlow with Keras. Corresponding PyTorch examples are provided online, and the book thereby covers the two dominating Python libraries for DL used in industry and academia. He concludes with an introduction to neural architecture search (NAS), exploring important ethical issues and providing resources for further learning. Explore and master core concepts: perceptrons, gradient-based learning, sigmoid neurons, and back propagation See how DL frameworks make it easier to develop more complicated and useful neural networks Discover how convolutional neural networks (CNNs) revolutionize image classification and analysis Apply recurrent neural networks (RNNs) and long short-term memory (LSTM) to text and other variable-length sequences Master NLP with sequence-to-sequence networks and the Transformer architecture Build applications for natural language translation and image captioning NVIDIA's invention of the GPU sparked the PC gaming market. The company's pioneering work in accelerated computing--a supercharged form of computing at the intersection of computer graphics, high-performance computing, and AI--is reshaping trillion-dollar industries, such as transportation, healthcare, and manufacturing, and fueling the growth of many others. Register your book for convenient access to downloads, updates, and/or corrections as they become available. See inside book for details.
  closed-form solution linear regression: Computer Vision – ACCV 2016 Shang-Hong Lai, Vincent Lepetit, Ko Nishino, Yoichi Sato, 2017-03-09 The five-volume set LNCS 10111-10115 constitutes the thoroughly refereed post-conference proceedings of the 13th Asian Conference on Computer Vision, ACCV 2016, held in Taipei, Taiwan, in November 2016. The total of 143 contributions presented in these volumes was carefully reviewed and selected from 479 submissions. The papers are organized in topical sections on Segmentation and Classification; Segmentation and Semantic Segmentation; Dictionary Learning, Retrieval, and Clustering; Deep Learning; People Tracking and Action Recognition; People and Actions; Faces; Computational Photography; Face and Gestures; Image Alignment; Computational Photography and Image Processing; Language and Video; 3D Computer Vision; Image Attributes, Language, and Recognition; Video Understanding; and 3D Vision.
  closed-form solution linear regression: Applied Statistics for the Social and Health Sciences Rachel A. Gordon, 2023-11-15 For graduate students in the social and health sciences, featuring essential concepts and equations most often needed in scholarly publications. Uses excerpts from the scholarly literature in these fields to introduce new concepts. Uses publicly-available data that are regularly used in social and health science publications to introduce Stata code and illustrate concepts and interpretation. Thoroughly integrates the teaching of statistical theory with teaching data processing and analysis. Offers guidance about planning projects and organizing code for reproducibility Shows how to recognize critiques of the constructions, terminology, and interpretations of statistics. New edition focuses on Stata, with code integrated into the chapters (rather than appendices, as in the first edition) includes Stata’s factor variables and margins commands and Long and Freese’s (2014) spost13 commands, to simplify programming and facilitate interpretation.
  closed-form solution linear regression: Machine Learners Adrian Mackenzie, 2017-11-16 If machine learning transforms the nature of knowledge, does it also transform the practice of critical thought? Machine learning—programming computers to learn from data—has spread across scientific disciplines, media, entertainment, and government. Medical research, autonomous vehicles, credit transaction processing, computer gaming, recommendation systems, finance, surveillance, and robotics use machine learning. Machine learning devices (sometimes understood as scientific models, sometimes as operational algorithms) anchor the field of data science. They have also become mundane mechanisms deeply embedded in a variety of systems and gadgets. In contexts from the everyday to the esoteric, machine learning is said to transform the nature of knowledge. In this book, Adrian Mackenzie investigates whether machine learning also transforms the practice of critical thinking. Mackenzie focuses on machine learners—either humans and machines or human-machine relations—situated among settings, data, and devices. The settings range from fMRI to Facebook; the data anything from cat images to DNA sequences; the devices include neural networks, support vector machines, and decision trees. He examines specific learning algorithms—writing code and writing about code—and develops an archaeology of operations that, following Foucault, views machine learning as a form of knowledge production and a strategy of power. Exploring layers of abstraction, data infrastructures, coding practices, diagrams, mathematical formalisms, and the social organization of machine learning, Mackenzie traces the mostly invisible architecture of one of the central zones of contemporary technological cultures. Mackenzie's account of machine learning locates places in which a sense of agency can take root. His archaeology of the operational formation of machine learning does not unearth the footprint of a strategic monolith but reveals the local tributaries of force that feed into the generalization and plurality of the field.
  closed-form solution linear regression: Statistical Computing Kennedy, 1980-03-01 This book provides an introduction to statistical computing and a critical, balanced presentation of the algorithms and computational methods used in software systems, discussing techniques for implementing algorithms in a computer. It is intended for graduate students in statistics.
  closed-form solution linear regression: Iterative Methods for Sparse Linear Systems Yousef Saad, 2003-04-01 Mathematics of Computing -- General.
  closed-form solution linear regression: Advances in Information Retrieval Mohand Boughanem, Catherine Berrut, Josiane Mothe, Chantal Soule-Dupuy, 2009-03-27 This book constitutes the refereed proceedings of the 30th annual European Conference on Information Retrieval Research, ECIR 2009, held in Toulouse, France in April 2009. The 42 revised full papers and 18 revised short papers presented together with the abstracts of 3 invited lectures and 25 poster papers were carefully reviewed and selected from 188 submissions. The papers are organized in topical sections on retrieval model, collaborative IR / filtering, learning, multimedia - metadata, expert search - advertising, evaluation, opinion detection, web IR, representation, clustering / categorization as well as distributed IR.
  closed-form solution linear regression: Artificial Intelligence Charu C. Aggarwal, 2021-07-16 This textbook covers the broader field of artificial intelligence. The chapters for this textbook span within three categories: Deductive reasoning methods: These methods start with pre-defined hypotheses and reason with them in order to arrive at logically sound conclusions. The underlying methods include search and logic-based methods. These methods are discussed in Chapters 1through 5. Inductive Learning Methods: These methods start with examples and use statistical methods in order to arrive at hypotheses. Examples include regression modeling, support vector machines, neural networks, reinforcement learning, unsupervised learning, and probabilistic graphical models. These methods are discussed in Chapters~6 through 11. Integrating Reasoning and Learning: Chapters~11 and 12 discuss techniques for integrating reasoning and learning. Examples include the use of knowledge graphs and neuro-symbolic artificial intelligence. The primary audience for this textbook are professors and advanced-level students in computer science. It is also possible to use this textbook for the mathematics requirements for an undergraduate data science course. Professionals working in this related field many also find this textbook useful as a reference.
  closed-form solution linear regression: Machine Learning Algorithms Fuwei Li, Lifeng Lai, Shuguang Cui, 2022-11-14 This book demonstrates the optimal adversarial attacks against several important signal processing algorithms. Through presenting the optimal attacks in wireless sensor networks, array signal processing, principal component analysis, etc, the authors reveal the robustness of the signal processing algorithms against adversarial attacks. Since data quality is crucial in signal processing, the adversary that can poison the data will be a significant threat to signal processing. Therefore, it is necessary and urgent to investigate the behavior of machine learning algorithms in signal processing under adversarial attacks. The authors in this book mainly examine the adversarial robustness of three commonly used machine learning algorithms in signal processing respectively: linear regression, LASSO-based feature selection, and principal component analysis (PCA). As to linear regression, the authors derive the optimal poisoning data sample and the optimal feature modifications, and also demonstrate the effectiveness of the attack against a wireless distributed learning system. The authors further extend the linear regression to LASSO-based feature selection and study the best strategy to mislead the learning system to select the wrong features. The authors find the optimal attack strategy by solving a bi-level optimization problem and also illustrate how this attack influences array signal processing and weather data analysis. In the end, the authors consider the adversarial robustness of the subspace learning problem. The authors examine the optimal modification strategy under the energy constraints to delude the PCA-based subspace learning algorithm. This book targets researchers working in machine learning, electronic information, and information theory as well as advanced-level students studying these subjects. R&D engineers who are working in machine learning, adversarial machine learning, robust machine learning, and technical consultants working on the security and robustness of machine learning are likely to purchase this book as a reference guide.
  closed-form solution linear regression: ECAI 2010 European Coordinating Committee for Artificial Intelligence, 2010 LC copy bound in 2 v.: v. 1, p. 1-509; v. 2, p. [509]-1153.
  closed-form solution linear regression: Robotics Research Antonio Bicchi, Wolfram Burgard, 2017-07-25 ISRR, the International Symposium on Robotics Research, is one of robotics pioneering Symposia, which has established over the past two decades some of the field's most fundamental and lasting contributions. This book presents the results of the seventeenth edition of Robotics Research ISRR15, offering a collection of a broad range of topics in robotics. The content of the contributions provides a wide coverage of the current state of robotics research.: the advances and challenges in its theoretical foundation and technology basis, and the developments in its traditional and new emerging areas of applications. The diversity, novelty, and span of the work unfolding in these areas reveal the field's increased maturity and expanded scope and define the state of the art of robotics and its future direction.
  closed-form solution linear regression: Unconventional Methods for Geoscience, Shale Gas and Petroleum in the 21st Century J. Watada, S.C. Tan, P.-C. Lin, 2023-09-11 Since the turn of the century, geology has advanced dramatically, with materials derived from extra-terrestrial sources meaning that it now encompasses cosmology, and new technologies providing ever more sophisticated possibilities for the conducting of research. This book, Unconventional Methods for Geoscience, Shale Gas and Petroleum in the 21st Century, aims to provide research directions for geology in the 21st century. As Eric Hobsbawm wrote, it is difficult to write the history of one’s own days, and selecting influential methods was no easy task, but an attempt has been made to include the most influential papers that represent the smart geology of the first few decades of the 21st century. The book presents 22 papers; the first serves as an introduction to biology, which is now expanding into the science of the cosmos following the discovery of previously missing information, and the remaining 21 papers are divided into 3 sections entitled Modelling, Simulation and Optimization. The importance of theoretical approaches from physics, mathematics, and statistics underlying meta-heuristic methods, knowledge and approaches is acknowledged, and there is a chapter dedicated to deep learning. The book contributes to the exploration of various possible solutions to challenging problems in both the Earth’s geology and that of the cosmos, and will be of interest to all those working in the field.
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Linear Regression Closed Form Solution (Download Only)
Linear Regression Closed Form Solution linear regression closed form solution: Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow Aurélien Géron, 2019-09-05 Through a series …

Linear Regression Closed Form Solution - finder-lbs.com
Implement the closed form solution of linear regression using Python in this second topic in the Data Science and Machine Learning Series. Follow along with Advait and start by importing the numpy, …

Linear Regression Closed Form Solution (2024) - finder …
Linear Regression Closed Form Solution: Data Science and Machine Learning Series Advait Jayant,2020 Follow along with machine learning expert Advait

Chapter 6
As previously stated, unlike a linear regression, we do not have a closed form solution for this problem. Instead, we must use an iterative method to find the global minimum for the function …

Closed form Maximum Likelihood Estimator for Generalized …
Regression models for heavy-tailed distributions have been mainly studied through the point-of-view of extreme value analysis, seeBeirlant et al.(2004) for a review. ... In a general setting, the …

Logistic Regression - cse.wustl.edu
Logistic regression is a common linear method for binary classification, and ... Unlike in linear regression, where there was a closed-form expression for the maximum-likelihood estimator, …

Linear Regression Closed Form Solution - finder-lbs.com
Linear Regression Closed Form Solution Christiaan Heij,Paul de Boer,Philip Hans Franses,Teun Kloek,Herman K. van Dijk,All at the Erasmus University in Rotterdam. Linear Regression Closed …

Lecture 8b: LASSO and Ridge regression - University of Oxford
I fitting a linear model of y on X I shrinking the coefficients; butthe nature of the l1 penalty causes some coefficients to be shrunken to zero exactly LASSO (vs. RIDGE): I LASSO performs variable …

CHAPTER Regression - Massachusetts Institute of Technology
Dec 18, 2019 · nd a closed-form formula for the answer! What does closed form mean? Generally, that it involves direct evaluation of a mathe-matical expression using a xed number of typ-ical …

CS 188 Introduction to Artificial Intelligence Spring 2024 Note …
Apr 2, 2024 · Linear regression has a celebrated closed form solution wˆ = (XT X)−1XT y, which we saw in the last note. However, we could have also chosen to solve for the optimal weights by …

Maximum Likelihood Estimation - H. Milton Stewart School of …
MotivationMaximum likelihood estimation (MLE)Non-linear least-squares estimation What if a closed-form solution does not exist /? In most practical models, there are twocomputational di …

Iterative Reweighted Least Squares - University at Buffalo
Linear and Logistic Regression •In linear regression there is a closed-form max likelihood solution for determining w •on the assumption of Gaussian noise model •Due to quadratic dependence of …

Inverse Optimization: Closed-form Solutions, Geometry …
Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization comprising a general inverse optimization model and a corresponding …

Machine Learning EE514 CS535 Linear Regression: …
Linear Regression: Formulation, Solutions, Polynomial Regression, Gradient Descent and Regularization Zubair Khalid School of Science and Engineering Lahore University of …

Linear models for forecasting arXiv:2403.14587v2 [cs.LG] 25 …
The convexity of least-squares linear regression suggests that the behaviour of these models should therefore be virtu-ally indistinguishable. We provide experimental evidence which …

Penalized Regression - WU
Regression coefficient estimates are available in closed form for a givenλ. LASSO: If λdecreases the coefficient values change in a piecewise linear fashion. The slope only changes if coefficients …

Solutions - CMU School of Computer Science
There is no closed form expression for maximizing the conditional log likelihood. One has to consider iterative optimization methods, such as gradient descent, to compute ^w. b)[5 pts.] For …

qwang@ethz.ch olga.fink@epfl.ch arXiv:2303.13325v1 …
closed-form ordinary least square (OLS) solution to the linear regressor in the deep domain adaptation context. Rather than aligning the original feature embedding space, we propose to …

CPSC 440: Advanced Machine Learning - Empirical Bayes
Bayesian Linear Regression Consider linear regression withGaussian likelihood and prior, yi˘N(wTxi;˙2); w j˘N(0; 1): MAP estimation in this model corresponds to L2-regularized linear …

Introduction to Machine Learning Lecture 15 - New York …
Ridge Regression Optimization problem: • directly based on generalization bound. • generalization of linear regression. • closed-form solution. • can be used with kernels. 9 where is a …

Least Squares Optimization with L1-Norm Regularization
Squares linear regression models with an L1 penalty on the regression coefficients. We first review linear regres-sion and regularization, and both motivate and formalize this problem. We then give …

Towards a Beter Understanding of Linear Models for …
the derivation and analysis of the closed-form solutions for two ba-sic regression and matrix factorization approaches, we found these two approaches are indeed inherently related but also …

Lecture 24{25: Weighted and Generalized Least Squares
When we use ordinary least squares to estimate linear regression, we (naturally) minimize the mean squared error: MSE(b) = 1 n Xn i=1 (y i x i ) 2 (1) The solution is of course b OLS= (x Tx) 1xTy (2) …

CS145 Discussion: Week 2 Linear Regression & Logistic …
Closed form solution. Linear Regression: Example A ball is rolled down a hallway and its position is recorded at five different ... Plug time values into linear regression equation Predicted value at …

Foundations of Machine Learning Regression - New York …
Ridge Regression Optimization problem: • directly based on generalization bound. • generalization of linear regression. • closed-form solution. • can be used with kernels. 23 where is a …

IEOR 265 – Lecture6 Lasso Regression - University of …
Lasso Regression 1 Lasso Regression The M-estimator which had the Bayesian interpretation of a linear model with Laplacian prior βˆ = argmin β kY −Xβk2 2 +λkβk 1, has multiple names: Lasso …

Logistic Regression - cs.rpi.edu
–Logistic regression LL is a concave function in •Unfortunately, the derivative becomes a transcendental equation, so it has no closed-form solution ☺ –Similar to non-linear least …

CS 229, Public Course Problem Set #2 Solutions: Theory
regression cost function is then J(θ) = 1 2 Xm i=1 (θTx(i) −y(i))2 + λ 2 kθk2. (a) Use the vector notation described in class to find a closed-form expreesion for the value of θ which minimizes …

Chapter 7 Least Squares Estimation - University of California, …
derivatives of S with respect to them yield equations that can be solved in closed form. Typically non-linear least squares problems do not provide a solution in closed form and one must resort …

Lecture notes on ridge regression - arXiv.org
First, linear regression is recaputilated. 1.1 Linear regression Consider an experiment in which pcharacteristics of nsamples are measured. The data from this experiment are denoted X, with X …

Q1-1: Which of the following statement is true about Linear …
1. Linear regression is sensitive to outliers 2. Linear regression is NOT sensitive to outliers 3. Can’t say 4. None of these The solution of the regression line will change due to outliers in most of the …

Ridge Regression - cs.umd.edu
NORMAL EQUATION - CLOSED FORM SOLUTION!20 1 2n[n ... For linear regression with regularization (ridge regression)

Lecture 12: Linear regression - Department of Computer …
2.2 Closed-form solution While gradient descent gives us one way of minimizing J(θ), the optimal parameters for the least squares objective can also be derived in a closed form. Here, we take …

Linear Regression - CMU School of Computer Science
Jan 26, 2006 · – Linear regression: • Linear in w, not in x! • This is linear: • This is also linear: – Nonlinear regression, e.g. ... Why linear regression? • MLE if the noise is independent Gaussian • …

plus ~40 awesome LAs
Ordinary least-square regression Closed-form solutions (when exists) Cases when closed-form solutions don't exist mathematically, practically, visually Regularization Hyperparameter and …

version or Normalization arXiv:2301.01854v2 [stat.ME] 26 Dec …
rately or altogether using the closed-form given. As immediate consequences, we also obtain a closed form for the generalized inverse, a closed-form for each of the coefficients of weighted …

High-Dimensional Regression: Ridge - University of California, …
High-Dimensional Regression: Ridge Advanced Topics in Statistical Learning, Spring 2023 Ryan Tibshirani ... inclosed-form(forgeneralH). However,inspecialcasesitis. …

Proceedings of the Twenty-Ninth AAAI Conference on Artificial …
low-rank regression model is equivalent to do regression in the subspace of each view. Matrix A is the subspace ma-trix of view . Matrix B is the shared regression parameter matrix of all views. …

Linear Models for Classification - University at Buffalo
•Analogous to regression: simple closed-form solution exists for parameters •Each C k ,k =1,..Kis described by its own linear model y k (x) = wT k x+ w k0 •Create augmented vector –replace x …

Lecture 7 Simple Linear Regression - Purdue University
Estimated Regression Line •Using the estimated parameters, the fitted regression line is Yˆ i= b0 + b1Xi where Yˆ i is the estimated value at Xi (Fitted value). •Fitted value Yˆ iis also an estimate of …

Chapter 3 Multiple Linear Regression Model The linear model …
Multiple Linear Regression Model We consider the problem of regression when the study variable depends on more than one explanatory or independent variables, called a multiple linear …

Abstract Introduction - GitHub Pages
4.1. Task 3.1. The below table summarizes our comparison of the closed-form solution linear regression and gradient descent approaches. We observe that in this case the closed-form …

A Machine Learning-based Approach for Solving Recurrence …
closed-form solution Approximate closed-form + Accuracy score (+) Counterexample yes no Fig. 1: Architecture of our novel machine learning-based recurrence solver. guarantees. We present the …

The theory of the generalized linear models - ku
The solution of this linear equation is hm+1 = hm h ¯k mY 1 khk 01 m Y¯ = hm U(h) U (hm) provided that U0(hm) 6= 0. This is Newton’s algorithm. With a suitable choice of starting value h1 we …

Regularization and Underconstrained Problems - University at …
1.Underconstrained closed-form solution 2.Underconstrained iterative solution 2.Regularization for Logistic Regression with linearly separable classes 3.Moore Penrose inverse 3. Deep Learning …

CS229 Lecture notes - Stanford Engineering Everywhere
If you’ve seen linear regression before, you may recognize this as the familiar least-squares cost function that gives rise to the ordinary least squares regression model. Whether or not you have …

10-701/15-781, Machine Learning: Homework 1 - CMU School …
Jan 21, 2010 · In linear regression, we are given training data of the form, D= (X;y) = f(x i;y i)g;i= 1;2;:::;N; where x ... in closed form and show that it is given by = (XTX+ I) 1XTy. [please, show …

Linear Regression - cs.rpi.edu
•Linear regression from a statistical point of view 2. Overview •Linear regression is one of the simplest and best understood methods in statistics/ML •We can derive closed-form optimal …

CHEAT SHEET Linear Regression - Amazon Web Services, Inc.
Linear Regression Algorithm Name Linear Regression Description Linear regression predicts a label of a given data point using a predicted “line” defi ned by w. The task is to learn this w by …

A Closed form expressions for the robust risks
A.1 Closed-form of robust risk for regression The following lemma provides a closed-form expression of the robust risk for the linear regression setting studied in Section 3. A similar result …