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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 확률과 통계 > 일반
· ISBN : 9781138046375
· 쪽수 : 376쪽
· 출판일 : 2019-01-29
목차
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
