TY - BOOK
AU - Arnold, Taylor
AU - Michael, Kane
AU - Lewis, Bryan W.
TI - A computational approach to statistical learning
SN - 9781138046375
U1 - 006.31015195
PY - 2019///
CY - Boca Raton
PB - CRC Press
KW - Machine learning - Mathematics
KW - Mathematical statistics
KW - Estimation theory
N1 - 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
N2 - 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.
https://www.crcpress.com/A-Computational-Approach-to-Statistical-Learning/Arnold-Kane-Lewis/p/book/9781138046375
ER -