Computational Approach to Statistical Learning

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

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• Aprendizagem mecânica
• Matemática para cientistas da computação
• Probabilidade e Estatística