Data Science and Machine Learning: Mathematical and Statistical Methods / Edition 1 available in Hardcover, eBook
Data Science and Machine Learning: Mathematical and Statistical Methods / Edition 1
 ISBN10:
 1138492531
 ISBN13:
 9781138492530
 Pub. Date:
 11/22/2019
 Publisher:
 CRC Press
 ISBN10:
 1138492531
 ISBN13:
 9781138492530
 Pub. Date:
 11/22/2019
 Publisher:
 CRC Press
Data Science and Machine Learning: Mathematical and Statistical Methods / Edition 1
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Overview
"This is a wellwritten book that provides a deeper dive into datascientific 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 selfcontained, accessible, and comprehensive.
 Extensive list of exercises and workedout examples.
 Many concrete algorithms with Python code.
 Full color throughout.
Further Resources can be found on the authors website: https://github.com/DSMLbook/Lectures
Product Details
ISBN13:  9781138492530 

Publisher:  CRC Press 
Publication date:  11/22/2019 
Series:  Chapman & Hall/CRC Machine Learning & Pattern Recognition 
Edition description:  New Edition 
Pages:  538 
Product dimensions:  8.25(w) x 11.00(h) x (d) 
About the Author
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 selfmixing 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.
Table of Contents
Preface Notation 1. Importing, Summarizing, and Visualizing Data 1.1 Introduction 1.2 Structuring Features According to Type 1.3 Summary Tables 1.4 Summary Statistics 1.5 Visualizing Data 1.5.1 Plotting Qualitative Variables 1.5.2 Plotting Quantitative Variables 1.5.3 Data Visualization in a Bivariate Setting Exercises 2. Statistical Learning 2.1 Introduction 2.2 Supervised and Unsupervised Learning 2.3 Training and Test Loss 2.4 Tradeoffs in Statistical Learning 2.5 Estimating Risk 2.5.1 InSample Risk 2.5.2 CrossValidation 2.6 Modeling Data 2.7 Multivariate Normal Models 2.8 Normal Linear Models 2.9 Bayesian Learning Exercises 3. Monte Carlo Methods 3.1 Introduction 3.2 Monte Carlo Sampling 3.2.1 Generating Random Numbers 3.2.2 Simulating Random Variables 3.2.3 Simulating Random Vectors and Processes 3.2.4 Resampling 3.2.5 Markov Chain Monte Carlo 3.3 Monte Carlo Estimation 3.3.1 Crude Monte Carlo 3.3.2 Bootstrap Method 3.3.3 Variance Reduction 3.4 Monte Carlo for Optimization 3.4.1 Simulated Annealing 3.4.2 CrossEntropy Method 3.4.3 Splitting for Optimization3.4.4 Noisy Optimization Exercises 4. Unsupervised Learning 4.1 Introduction 4.2 Risk and Loss in Unsupervised Learning 4.3 Expectation–Maximization (EM) Algorithm 4.4 Empirical Distribution and Density Estimation 4.5 Clustering via Mixture Models 4.5.1 Mixture Models 4.5.2 EM Algorithm for Mixture Models 4.6 Clustering via Vector Quantization 4.6.1 KMeans 4.6.2 Clustering via Continuous Multiextremal Optimization 4.7 Hierarchical Clustering 4.8 Principal Component Analysis (PCA) 4.8.1 Motivation: Principal Axes of an Ellipsoid 4.8.2 PCA and Singular Value Decomposition (SVD) Exercises 5. Regression 5.1 Introduction 5.2 Linear Regression 5.3 Analysis via Linear Models 5.3.1 Parameter Estimation 5.3.2 Model Selection and Prediction 5.3.3 CrossValidation and Predictive Residual Sum of Squares 5.3.4 InSample Risk and Akaike Information Criterion 5.3.5 Categorical Features 5.3.6 Nested Models 5.3.7 Coefficient of Determination 5.4 Inference for Normal Linear Models 5.4.1 Comparing Two Normal Linear Models 5.4.2 Confidence and Prediction Intervals 5.5 Nonlinear Regression Models 5.6 Linear Models in Python 5.6.1 Modeling 5.6.2 Analysis 5.6.3 Analysis of Variance (ANOVA) 5.6.4 Confidence and Prediction Intervals 5.6.5 Model Validation 5.6.6 Variable Selection 5.7 Generalized Linear Models Exercises 6. Regularization and Kernel Methods 6.1 Introduction 6.2 Regularization 6.3 Reproducing Kernel Hilbert Spaces 6.4 Construction of Reproducing Kernels 6.4.1 Reproducing Kernels via Feature Mapping 6.4.2 Kernels from Characteristic Functions 6.4.3 Reproducing Kernels Using Orthonormal Features 6.4.4 Kernels from Kernels 6.5 Representer Theorem 6.6 Smoothing Cubic Splines 6.7 Gaussian Process Regression 6.8 Kernel PCA Exercises 7. Classification 7.1 Introduction 7.2 Classification Metrics 7.3 Classification via Bayes’ Rule 7.4 Linear and Quadratic Discriminant Analysis 7.5 Logistic Regression and Softmax Classification 7.6 Knearest Neighbors Classification 7.7 Support Vector Machine 7.8 Classification with ScikitLearn Exercises 8. Decision Trees and Ensemble Methods 8.1 Introduction 8.2 TopDown Construction of Decision Trees 8.2.1 Regional Prediction Functions 8.2.2 Splitting Rules 8.2.3 Termination Criterion 8.2.4 Basic Implementation 8.3 Additional Considerations 8.3.1 Binary Versus NonBinary Trees 8.3.2 Data Preprocessing 8.3.3 Alternative Splitting Rules 8.3.4 Categorical Variables 8.3.5 Missing Values 8.4 Controlling the Tree Shape 8.4.1 CostComplexity Pruning 8.4.2 Advantages and Limitations of Decision Trees 8.5 Bootstrap Aggregation 8.6 Random Forests 8.7 Boosting Exercises 9. Deep Learning 9.1 Introduction 9.2 FeedForward Neural Networks 9.3 BackPropagation 9.4 Methods for Training 9.4.1 Steepest Descent 9.4.2 Levenberg–Marquardt Method 9.4.3 LimitedMemory BFGS Method 9.4.4 Adaptive Gradient Methods 9.5 Examples in Python 9.5.1 Simple Polynomial Regression 9.5.2 Image Classification Exercises A. Linear Algebra and Functional Analysis A.1 Vector Spaces, Bases, and Matrices A.2 Inner Product A.3 Complex Vectors and Matrices A.4 Orthogonal Projections A.5 Eigenvalues and Eigenvectors A.5.1 Left and RightEigenvectors A.6 Matrix Decompositions A.6.1 (P)LU Decomposition A.6.2 Woodbury Identity A.6.3 Cholesky Decomposition A.6.4 QR Decomposition and the Gram–Schmidt Procedure A.6.5 Singular Value Decomposition A.6.6 Solving Structured Matrix Equations A.7 Functional Analysis A.8 Fourier Transforms A.8.1 Discrete Fourier Transform A.8.2 Fast Fourier Transform B. Multivariate Differentiation and Optimization B.1 Multivariate Differentiation B.1.1 Taylor Expansion B.1.2 Chain Rule B.2 Optimization Theory B.2.1 Convexity and Optimization B.2.2 Lagrangian Method B.2.3 Duality B.3 Numerical RootFinding and Minimization B.3.1 NewtonLike Methods B.3.2 QuasiNewton Methods B.3.3 Normal Approximation Method B.3.4 Nonlinear Least Squares B.4 Constrained Minimization via Penalty Functions C. Probability and Statistics C.1 Random Experiments and Probability Spaces C.2 Random Variables and Probability Distributions C.3 Expectation C.4 Joint Distributions C.5 Conditioning and Independence C.5.1 Conditional Probability C.5.2 Independence C.5.3 Expectation and Covariance C.5.4 Conditional Density and Conditional Expectation C.6 Functions of Random Variables C.7 Multivariate Normal Distribution C.8 Convergence of Random Variables C.9 Law of Large Numbers and Central Limit Theorem C.10 Markov Chains C.11 Statistics C.12 Estimation C.12.1 Method of Moments C.12.2 Maximum Likelihood Method C.13 Confidence Intervals C.14 Hypothesis Testing D. Python Primer D.1 Getting Started D.2 Python Objects D.3 Types and Operators D.4 Functions and Methods D.5 Modules D.6 Flow Control D.7 Iteration D.8 Classes D.9 Files D.10 NumPy D.10.1 Creating and Shaping Arrays D.10.2 Slicing D.10.3 Array Operations D.10.4 Random Numbers D.11 Matplotlib D.11.1 Creating a Basic Plot D.12 Pandas D.12.1 Series and DataFrame D.12.2 Manipulating Data Frames D.12.3 Extracting Information D.12.4 Plotting D.13 Scikitlearn D.13.1 Partitioning the Data D.13.2 Standardization D.13.3 Fitting and Prediction D.13.4 Testing the Model D.14 System Calls, URL Access, and SpeedUp Bibliography Index