A Computational Approach to Statistical Learning: 1st Edition (Hardback) book cover

A Computational Approach to Statistical Learning

1st Edition

By Taylor Arnold, Michael Kane, Bryan W. Lewis

Chapman and Hall/CRC

362 pages

Purchasing Options:$ = USD
Hardback: 9781138046375
pub: 2019-01-29
SAVE ~$19.99
$99.95
$79.96
x
eBook (VitalSource) : 9781315171401
pub: 2019-01-23
from $49.98


FREE Standard Shipping!

Description

A Computational Approach to Statistical Learning gives a novel introduction to predictive modeling by focusing on the algorithmic and numeric motivations behind popular statistical methods. The text contains annotated code to over 80 original reference functions. These functions provide minimal working implementations of common statistical learning algorithms. Every chapter concludes with a fully worked out application that illustrates predictive modeling tasks using a real-world dataset.

The text begins with a detailed analysis of linear models and ordinary least squares. Subsequent chapters explore extensions such as ridge regression, generalized linear models, and additive models. The second half focuses on the use of general-purpose algorithms for convex optimization and their application to tasks in statistical learning. Models covered include the elastic net, dense neural networks, convolutional neural networks (CNNs), and spectral clustering. A unifying theme throughout the text is the use of optimization theory in the description of predictive models, with a particular focus on the singular value decomposition (SVD). Through this theme, the computational approach motivates and clarifies the relationships between various predictive models.

Taylor Arnold is an assistant professor of statistics at the University of Richmond. His work at the intersection of computer vision, natural language processing, and digital humanities has been supported by multiple grants from the National Endowment for the Humanities (NEH) and the American Council of Learned Societies (ACLS). His first book, Humanities Data in R, was published in 2015.

Michael Kane is an assistant professor of biostatistics at Yale University. He is the recipient of grants from the National Institutes of Health (NIH), DARPA, and the Bill and Melinda Gates Foundation. His R package bigmemory won the Chamber's prize for statistical software in 2010.

Bryan Lewis is an applied mathematician and author of many popular R packages, including irlba, doRedis, and threejs.

Reviews

"As best as I can determine, ‘A Computational Approach to Statistical Learning’ (CASL) is unique among R books devoted to statistical learning and data science. Other popular texts…cover much of the same ground, and include extensive R code implementing statistical models. What makes CASL different is the unifying mathematical structure underlying the presentation and the focus on the computations themselves…CASL’s great strengths are the use linear algebra to provide a coherent, unifying mathematical framework for explaining a wide class of models, a lucid writing style that appeals to geometric intuition, clear explanations of many details that are mostly glossed over in more superficial treatments, the inclusion of historical references, and R code that is tightly integrated into the text. The R code is extensive, concise without being opaque, and in many cases, elegant. The code illustrates R’s advantages for developing statistical algorithms as well as its power to present versatile and compelling visualizations…CASL ought to appeal to anyone working in data science or machine learning seeking a sophisticated understanding of both the theoretical basis and efficient algorithms underlying a modern approach to computational statistics."

~Joe Rickert, RStudio

"The ‘literate programming’ style is my favorite part of this book (borrowing the term from Don Knuth). It would be well suited for an engineer seeking to understand the implementations and ideas behind these statistical models. Real code beats pseudocode, because one can easily tweak and experiment with it…The other part I especially like is the development of neural nets based on extending the models previously introduced in the text. This takes some of the mystery out of neural nets and makes them more accessible to a statistician studying them for the first time… I would happily buy this book for my own reference and self-study… I’m not aware of any books that are written at this level that combines the motivation, the mathematics and the code in such a nice way. If I ever happen to be teaching a course on this material, then I would definitely teach from this book."

~Clark Fitzgerald, University of California, Davis

"I think the book is quite clearly written and covers really important things to consider that can help optimize model building. The book does a really great job of following its theme throughout and explicitly mentioning why they are explaining something the way they explain it. Reading the book, it is clear they considered how all the parts the included (at least the chapters I read) fit into the broader scope of the book's goal."

~Justin Post, North Carolina State University

Table of Contents

1. Introduction

Computational approach

Statistical learning

Example

Prerequisites

How to read this book

Supplementary materials

Formalisms and terminology

Exercises

2. Linear Models

Introduction

Ordinary least squares

The normal equations

Solving least squares with the singular value decomposition

Directly solving the linear system

(?) Solving linear models with orthogonal projection

(?) Sensitivity analysis

(?) Relationship between numerical and statistical error

Implementation and notes

Application: Cancer incidence rates

Exercises

3. Ridge Regression and Principal Component Analysis

Variance in OLS

Ridge regression

(?) A Bayesian perspective

Principal component analysis

Implementation and notes

Application: NYC taxicab data

Exercises

4. Linear Smoothers

Non-linearity

Basis expansion

Kernel regression

Local regression

Regression splines

(?) Smoothing splines

(?) B-splines

Implementation and notes

Application: US census tract data

Exercises

5. Generalized Linear Models

Classification with linear models

Exponential families

Iteratively reweighted GLMs

(?) Numerical issues

(?) Multi-class regression

Implementation and notes

Application: Chicago crime prediction

Exercises

6. Additive Models

Multivariate linear smoothers

Curse of dimensionality

Additive models

(?) Additive models as linear models

(?) Standard errors in additive models

Implementation and notes

Application: NYC flights data

Exercises

7. Penalized Regression Models

Variable selection

Penalized regression with the `- and `-norms

Orthogonal data matrix

Convex optimization and the elastic net

Coordinate descent

(?) Active set screening using the KKT conditions

(?) The generalized elastic net model

Implementation and notes

Application: Amazon product reviews

Exercises

8. Neural Networks

Dense neural network architecture

Stochastic gradient descent

Backward propagation of errors

Implementing backpropagation

Recognizing hand written digits

(?) Improving SGD and regularization

(?) Classification with neural networks

(?) Convolutional neural networks

Implementation and notes

Application: Image classification with EMNIST

Exercises

9. Dimensionality Reduction

Unsupervised learning

Kernel functions

Kernel principal component analysis

Spectral clustering

t-Distributed stochastic neighbor embedding (t-SNE)

Autoencoders

Implementation and notes

Application: Classifying and visualizing fashion MNIST

Exercises

10. Computation in Practice

Reference implementations

Sparse matrices

Sparse generalized linear models

Computation on row chunks

Feature hashing

Data quality issues

Implementation and notes

Application

Exercises

A Matrix Algebra

A Vector spaces

A Matrices

A Other useful matrix decompositions

B Floating Point Arithmetic and Numerical Computation

B Floating point arithmetic

B Numerical sources of error

B Computational effort

About the Authors

Taylor Arnold is an assistant professor of statistics at the University of Richmond. His work at the intersection of computer vision, natural language processing, and digital humanities has been supported by multiple grants from the National Endowment for the Humanities (NEH) and the American Council of Learned Societies (ACLS). His first book, Humanities Data in R, was published in 2015.

Michael Kane is an assistant professor of biostatistics at Yale University. He is the recipient of grants from the National Institutes of Health (NIH), DARPA, and the Bill and Melinda Gates Foundation. His R package bigmemory won the Chamber's prize for statistical software in 2010.

Bryan Lewis is an applied mathematician and author of many popular R packages, including irlba, doRedis, and threejs.

About the Series

Chapman & Hall/CRC Texts in Statistical Science

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
BUS061000
BUSINESS & ECONOMICS / Statistics
COM000000
COMPUTERS / General
COM037000
COMPUTERS / Machine Theory