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Data Science and Machine Learning: Mathematical and Statistical Methods [Hardback]

4.60/5 (10 ratings by Goodreads)
(University of Wales Trinity Saint David, Hong Kong)
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Data Science and Machine Learning: Mathematical and Statistical MethodsPalielināt
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781138492530.html
Keywords:

"This textbook is a well-rounded, rigorous, and informative work presenting the mathematics behind modern machine learning techniques. It hits all the right notes: the choice of topics is up-to-date and perfect for a course on data science for mathematics students at the advanced undergraduate or early graduate level. This book fills a sorely-needed gap in the existing literature by not sacrificing depth for breadth, presenting proofs of major theorems and subsequent derivations, as well as providing a copious amount of Python code. I only wish a book like this had been around when I first began my journey!" -Nicholas Hoell, University of Toronto

"This is a well-written book that provides a deeper dive into data-scientific methods than many introductory texts. The writing is clear, and the text logically builds up regularization, classification, and decision trees. Compared to its probable competitors, it carves out a unique niche.

-Adam Loy, Carleton College

The purpose of Data Science and Machine Learning: Mathematical and Statistical Methods is to provide an accessible, yet comprehensive textbook intended for students interested in gaining a better understanding of the mathematics and statistics that underpin the rich variety of ideas and machine learning algorithms in data science.

Key Features:

  • Focuses on mathematical understanding.

  • Presentation is self-contained, accessible, and comprehensive.

  • Extensive list of exercises and worked-out examples.

  • Many concrete algorithms with Python code.

    • Full color throughout.

    • The Authors:

    Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics at The University of Queensland. He has published over 120 articles and five books in a wide range of areas in mathematics, statistics, data science, machine learning, and Monte Carlo methods. He is a pioneer of the well-known Cross-Entropy method—an adaptive Monte Carlo technique, which is being used around the world to help solve difficult estimation and optimization problems in science, engineering, and finance.

    Zdravko Botev

    , PhD

    , is an Australian Mathematical Science Institute Lecturer in Data Science and Machine Learning with an appointment at the University of New South Wales in Sydney, Australia. He is the recipient of the 2018 Christopher Heyde Medal of the Australian Academy of Science for distinguished research in the Mathematical Sciences.

    Thomas Taimre

    , PhD

    , is a Senior Lecturer of Mathematics and Statistics at The University of Queensland. His research interests range from applied probability and Monte Carlo methods to applied physics and the remarkably universal self-mixing effect in lasers. He has published over 100 articles, holds a patent, and is the coauthor of Handbook of Monte Carlo Methods (Wiley).

    Radislav Vaisman, PhD, is a Lecturer of Mathematics and Statistics at The University of Queensland. His research interests lie at the intersection of applied probability, machine learning, and computer science. He has published over 20 articles and two books.

    Recenzijas

    "The first impression when handling and opening this book at a random page is superb. A big format (A4) and heavy weight, because the paper quality is high, along with a spectacular style and large font, much colour and many plots, and blocks of python code enhanced in colour boxes. This makes the book attractive and easy to study...The book is a very well-designed data science course, with mathematical rigor in mind. Key concepts are highlighted in red in the margins, often with links to other parts of the book...This book will be excellent for those that want to build a strong mathematical foundation for their knowledge on the main machine learning techniques, and at the same time get python recipes on how to perform the analyses for worked examples." - Victor Moreno, ISCB News, December 2020 'The way the Python code was written follows the algorithm closely. This is very useful for readers who wish to understand the rationale and flow of the background knowledge. In each chapter, the authors recommend further readings for those who plan to learn advanced topics. Another useful part is that the Python implementation of different statistical learning algorithms is discussed throughout the book. At the end of each chapter, extensive exercises are designed. These exercises can help readers understand the content better. This book would be a good reference for readers who are already experienced with statistical analysis and are looking for theoretical background knowledge of the algorithms.'

    -Yin-Ju Lai and Chuhsing Kate Hsiao, Biometrics, vol 77, issue 4, 2021

    Preface xiii
    Notation xvii
    1 Importing, Summarizing, and Visualizing Data
    		1(18)
    1.1 Introduction
    		1(2)
    1.2 Structuring Features According to Type
    		3(3)
    1.3 Summary Tables
    		6(1)
    1.4 Summary Statistics
    		7(1)
    1.5 Visualizing Data
    		8(7)
    1.5.1 Plotting Qualitative Variables
    		9(1)
    1.5.2 Plotting Quantitative Variables
    		9(3)
    1.5.3 Data Visualization in a Bivariate Setting
    		12(3)
    Exercises
    		15(4)
    2 Statistical Learning
    		19(48)
    2.1 Introduction
    		19(1)
    2.2 Supervised and Unsupervised Learning
    		20(3)
    2.3 Training and Test Loss
    		23(8)
    2.4 Tradeoffs in Statistical Learning
    		31(4)
    2.5 Estimating Risk
    		35(5)
    2.5.1 In-Sample Risk
    		35(2)
    2.5.2 Cross-Validation
    		37(3)
    2.6 Modeling Data
    		40(4)
    2.7 Multivariate Normal Models
    		44(2)
    2.8 Normal Linear Models
    		46(1)
    2.9 Bayesian Learning
    		47(11)
    Exercises
    		58(9)
    3 Monte Carlo Methods
    		67(54)
    3.1 Introduction
    		67(1)
    3.2 Monte Carlo Sampling
    		68(17)
    3.2.1 Generating Random Numbers
    		68(1)
    3.2.2 Simulating Random Variables
    		69(5)
    3.2.3 Simulating Random Vectors and Processes
    		74(2)
    3.2.4 Resampling
    		76(2)
    3.2.5 Markov Chain Monte Carlo
    		78(7)
    3.3 Monte Carlo Estimation
    		85(11)
    3.3.1 Crude Monte Carlo
    		85(3)
    3.3.2 Bootstrap Method
    		88(4)
    3.3.3 Variance Reduction
    		92(4)
    3.4 Monte Carlo for Optimization
    		96(17)
    3.4.1 Simulated Annealing
    		96(4)
    3.4.2 Cross-Entropy Method
    		100(3)
    3.4.3 Splitting for Optimization
    		103(2)
    3.4.4 Noisy Optimization
    		105(8)
    Exercises
    		113(8)
    4 Unsupervised Learning
    		121(46)
    4.1 Introduction
    		121(1)
    4.2 Risk and Loss in Unsupervised Learning
    		122(6)
    4.3 Expectation-Maximization (EM) Algorithm
    		128(3)
    4.4 Empirical Distribution and Density Estimation
    		131(4)
    4.5 Clustering via Mixture Models
    		135(7)
    4.5.1 Mixture Models
    		135(2)
    4.5.2 EM Algorithm for Mixture Models
    		137(5)
    4.6 Clustering via Vector Quantization
    		142(5)
    4.6.1 tf-Means
    		144(2)
    4.6.2 Clustering via Continuous Multiextremal Optimization
    		146(1)
    4.7 Hierarchical Clustering
    		147(6)
    4.8 Principal Component Analysis (PCA)
    		153(7)
    4.8.1 Motivation: Principal Axes of an Ellipsoid
    		153(2)
    4.8.2 PCA and Singular Value Decomposition (SVD)
    		155(5)
    Exercises
    		160(7)
    5 Regression
    		167(48)
    5.1 Introduction
    		167(2)
    5.2 Linear Regression
    		169(2)
    5.3 Analysis via Linear Models
    		171(11)
    5.3.1 Parameter Estimation
    		171(1)
    5.3.2 Model Selection and Prediction
    		172(1)
    5.3.3 Cross-Validation and Predictive Residual Sum of Squares
    		173(2)
    5.3.4 In-Sample Risk and Akaike Information Criterion
    		175(2)
    5.3.5 Categorical Features
    		177(3)
    5.3.6 Nested Models
    		180(1)
    5.3.7 Coefficient of Determination
    		181(1)
    5.4 Inference for Normal Linear Models
    		182(6)
    5.4.1 Comparing Two Normal Linear Models
    		183(3)
    5.4.2 Confidence and Prediction Intervals
    		186(2)
    5.5 Nonlinear Regression Models
    		188(3)
    5.6 Linear Models in Python
    		191(13)
    5.6.1 Modeling
    		191(2)
    5.6.2 Analysis
    		193(2)
    5.6.3 Analysis of Variance (ANOVA)
    		195(3)
    5.6.4 Confidence and Prediction Intervals
    		198(1)
    5.6.5 Model Validation
    		198(1)
    5.6.6 Variable Selection
    		199(5)
    5.7 Generalized Linear Models
    		204(3)
    Exercises
    		207(8)
    6 Regularization and Kernel Methods
    		215(36)
    6.1 Introduction
    		215(1)
    6.2 Regularization
    		216(6)
    6.3 Reproducing Kernel Hilbert Spaces
    		222(2)
    6.4 Construction of Reproducing Kernels
    		224(6)
    6.4.1 Reproducing Kernels via Feature Mapping
    		224(1)
    6.4.2 Kernels from Characteristic Functions
    		225(2)
    6.4.3 Reproducing Kernels Using Orthonormal Features
    		227(2)
    6.4.4 Kernels from Kernels
    		229(1)
    6.5 Representer Theorem
    		230(5)
    6.6 Smoothing Cubic Splines
    		235(3)
    6.7 Gaussian Process Regression
    		238(4)
    6.8 Kernel PCA
    		242(3)
    Exercises
    		245(6)
    7 Classification
    		251(36)
    7.1 Introduction
    		251(2)
    7.2 Classification Metrics
    		253(4)
    7.3 Classification via Bayes' Rule
    		257(2)
    7.4 Linear and Quadratic Discriminant Analysis
    		259(7)
    7.5 Logistic Regression and Softmax Classification
    		266(2)
    7.6 k-Nearest Neighbors Classification
    		268(1)
    7.7 Support Vector Machine
    		269(8)
    7.8 Classification with Scikit-Learn
    		277(2)
    Exercises
    		279(8)
    8 Decision Trees and Ensemble Methods
    		287(36)
    8.1 Introduction
    		287(2)
    8.2 Top-Down Construction of Decision Trees
    		289(9)
    8.2.1 Regional Prediction Functions
    		290(1)
    8.2.2 Splitting Rules
    		291(1)
    8.2.3 Termination Criterion
    		292(2)
    8.2.4 Basic Implementation
    		294(4)
    8.3 Additional Considerations
    		298(2)
    8.3.1 Binary Versus Non-Binary Trees
    		298(1)
    8.3.2 Data Preprocessing
    		298(1)
    8.3.3 Alternative Splitting Rules
    		298(1)
    8.3.4 Categorical Variables
    		299(1)
    8.3.5 Missing Values
    		299(1)
    8.4 Controlling the Tree Shape
    		300(5)
    8.4.1 Cost-Complexity Pruning
    		303(1)
    8.4.2 Advantages and Limitations of Decision Trees
    		304(1)
    8.5 Bootstrap Aggregation
    		305(4)
    8.6 Random Forests
    		309(4)
    8.7 Boosting
    		313(8)
    Exercises
    		321(2)
    9 Deep Learning
    		323(32)
    9.1 Introduction
    		323(3)
    9.2 Feed-Forward Neural Networks
    		326(4)
    9.3 Back-Propagation
    		330(4)
    9.4 Methods for Training
    		334(6)
    9.4.1 Steepest Descent
    		334(1)
    9.4.2 Levenberg-Marquardt Method
    		335(1)
    9.4.3 Limited-Memory BFGS Method
    		336(2)
    9.4.4 Adaptive Gradient Methods
    		338(2)
    9.5 Examples in Python
    		340(9)
    9.5.1 Simple Polynomial Regression
    		340(4)
    9.5.2 Image Classification
    		344(5)
    Exercises
    		349(6)
    A Linear Algebra and Functional Analysis
    		355(42)
    A.1 Vector Spaces, Bases, and Matrices
    		355(5)
    A.2 Inner Product
    		360(1)
    A.3 Complex Vectors and Matrices
    		361(1)
    A.4 Orthogonal Projections
    		362(1)
    A.5 Eigenvalues and Eigenvectors
    		363(5)
    A.5.2 Left-and Right-Eigenvectors
    		364(4)
    A.6 Matrix Decompositions
    		368(16)
    A.6.2 (P)LU Decomposition
    		368(2)
    A.6.2 Woodbury Identity
    		370(3)
    A.6.3 Cholesky Decomposition
    		373(2)
    A.6.4 QR Decomposition and the Gram-Schmidt Procedure
    		375(1)
    A.6.5 Singular Value Decomposition
    		376(3)
    A.6.6 Solving Structured Matrix Equations
    		379(5)
    A.7 Functional Analysis
    		384(6)
    A.8 Fourier Transforms
    		390(7)
    A.8.2 Discrete Fourier Transform
    		392(2)
    A.8.2 Fast Fourier Transform
    		394(3)
    B Multivariate Differentiation and Optimization
    		397(24)
    B.1 Multivariate Differentiation
    		397(5)
    B.1.1 Taylor Expansion
    		400(1)
    B.1.2 Chain Rule
    		400(2)
    B.2 Optimization Theory
    		402(6)
    B.2.2 Convexity and Optimization
    		403(3)
    B.2.2 Lagrangian Method
    		406(1)
    B.2.3 Duality
    		407(1)
    B.3 Numerical Root-Finding and Minimization
    		408(7)
    B.3.2 Newton-Like Methods
    		409(2)
    B.3.2 Quasi-Newton Methods
    		411(2)
    B.3.3 Normal Approximation Method
    		413(1)
    B.3.4 Nonlinear Least Squares
    		414(1)
    B.4 Constrained Minimization via Penalty Functions
    		415(6)
    C Probability and Statistics
    		421(42)
    C.1 Random Experiments and Probability Spaces
    		421(1)
    C.2 Random Variables and Probability Distributions
    		422(4)
    C.3 Expectation
    		426(1)
    C.4 Joint Distributions
    		427(1)
    C.5 Conditioning and Independence
    		428(3)
    C.5.1 Conditional Probability
    		428(1)
    C.5.2 Independence
    		428(1)
    C.5.3 Expectation and Covariance
    		429(1)
    C.5.4 Conditional Density and Conditional Expectation
    		430(1)
    C.6 Functions of Random Variables
    		431(3)
    C.7 Multivariate Normal Distribution
    		434(5)
    C.8 Convergence of Random Variables
    		439(6)
    C.9 Law of Large Numbers and Central Limit Theorem
    		445(6)
    C.10 Markov Chains
    		451(2)
    C.11 Statistics
    		453(1)
    C.12 Estimation
    		454(3)
    C.12.1 Method of Moments
    		455(1)
    C.12.2 Maximum Likelihood Method
    		456(1)
    C.13 Confidence Intervals
    		457(1)
    C.14 Hypothesis Testing
    		458(5)
    D Python Primer
    		463(32)
    D.1 Getting Started
    		463(2)
    D.2 Python Objects
    		465(1)
    D.3 Types and Operators
    		466(2)
    D.4 Functions and Methods
    		468(1)
    D.5 Modules
    		469(2)
    D.6 Flow Control
    		471(1)
    D.7 Iteration
    		472(1)
    D.8 Classes
    		473(2)
    D.9 Files
    		475(3)
    D.10 NumPy
    		478(5)
    D.10.1 Creating and Shaping Arrays
    		478(2)
    D.10.2 Slicing
    		480(1)
    D.10.3 Array Operations
    		480(2)
    D.l0.4 Random Numbers
    		482(1)
    D.11 Matplotlib
    		483(2)
    D.11.1 Creating a Basic Plot
    		483(2)
    D.12 Pandas
    		485(5)
    D.12.1 Series and DataFrame
    		485(2)
    D.12.2 Manipulating Data Frames
    		487(1)
    D.12.3 Extracting Information
    		488(2)
    D.12.4 Plotting
    		490(1)
    D.13 Scikit-learn
    		490(3)
    D.13.1 Partitioning the Data
    		491(1)
    D.13.2 Standardization
    		491(1)
    D.13.3 Fitting and Prediction
    		492(1)
    D.13.4 Testing the Model
    		492(1)
    D.14 System Calls, URL Access, and Speed-Up
    		493(2)
    Bibliography 495(8)
    Index 503
    Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics at The University of Queensland. He has published over 120 articles and five books in a wide range of areas in mathematics, statistics, data science, machine learning, and Monte Carlo methods. He is a pioneer of the well-known Cross-Entropy methodan adaptive Monte Carlo technique, which is being used around the world to help solve difficult estimation and optimization problems in science, engineering, and finance.

    Zdravko Botev, PhD, is an Australian Mathematical Science Institute Lecturer in Data Science and Machine Learning with an appointment at the University of New South Wales in Sydney, Australia. He is the recipient of the 2018 Christopher Heyde Medal of the Australian Academy of Science for distinguished research in the Mathematical Sciences.

    Thomas Taimre, PhD, is a Senior Lecturer of Mathematics and Statistics at The University of Queensland. His research interests range from applied probability and Monte Carlo methods to applied physics and the remarkably universal self-mixing effect in lasers. He has published over 100 articles, holds a patent, and is the coauthor of Handbook of Monte Carlo Methods (Wiley).

    Radislav Vaisman, PhD, is a Lecturer of Mathematics and Statistics at The University of Queensland. His research interests lie at the intersection of applied probability, machine learning, and computer science. He has published over 20 articles and two books.