We will use the following textbooks for this course:
[HTF] The elements of statistical learning: data mining, inference and prediction. Trevor Hastie, Robert Tibshirani and Jerome Friedman. Springer. 2001. Q325.75.F75 2001 c. 1. Available at http://statweb.stanford.edu/~tibs/ElemStatLearn/.
[BIS] Pattern recognition and machine learning. Christopher M. Bishop. 2009. Q327.B52 2009 c. 1
Other useful references are:
[MRT] Foundations of machine learning. Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. 2012. Q325.5 .M64 2012 c. 1
[SSBD] Understanding Machine Learning: From Theory to Algorithms. Shai ShalevShwartz and Shai BenDavid. 2014. Q325.5 .S475 2014 c. 1. Available at http://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/understandingmachinelearningtheoryalgorithms.pdf.
[MUR] Machine learning: a probabilistic perspective. Kevin P. Murphy. 2012. Q325.5 .M87 2012 c. 1
[TM] Machine learning. Tom M. Mitchell. 1997. Q325.5.M58 1997 c. 1
Date 
Topics 
Readings 

Introduction 

T 
Introduction to Machine Learning Define learning, why/when do we need machine learning, discuss different types of machine learning, recent success, cool applications 
MUR Chapter 1 PDF, 

Th 
Course overview, formal introduction Supervised learning: task, performance, evaluation; classification, regression, loss function, risk 
MRT Chapter 1 

F 
Recitation: Probability and Statistics Events, random variables, probabilities, pdf, pmf, cdf, mean, mode, median, variance, multivariate distributions, marginals, conditionals, Bayes theorem, independence 
Review slides


T 
Foundations Bayes optimal rule, Bayes risk, empirical risk minimization (ERM), generalization error, supervised learning: classification/regression, rote learning, lazy learning, model fitting 
SSBD Chapter 2, HTF Section 2.12.3, MUR Sections 1.11.2 

Th 
Recitation: Linear Algebra Vector spaces, norms, metric spaces, inner product spaces, CauchySchwarz, Orthonormal bases 

F 
Recitation: MLE, MAP, Intro Python
Parametric distributions, parameter estimation (MLE), MAP; introduction to Python, Jupyter notebook, numpy 
BIS Chapter 2,


T 
Linear Regression Linear functions, loss function, empirical risk minimization, least squares solution, generalization, error decomposition 
HTF Sections 2.3, 3.2,
BIS Section 3.1 

Th 
Error analysis, statistical view Bayes optimal predictor, statistical view, Gaussian model, Maximum Likelihood Estimation (MLE), Polynomial regression, general additive regression, overfitting 
HTF Sections 2.4, 2.6, 2.9, BIS Sections 1.1,
1.2, 3.1, 3.2, MUR Sections 7.17.3, SSBD Section 9.2,


F 
Gradient descent; biasvariance tradeoff Gradient ascent/descent, stepsize, convergence, Bias of an estimator, consistency, estimation and regression, biasvariance decomposition in regression, Cramer Rao inequality, Fisher information 


T 
Regularization Model complexity and overfitting, penalizing model complexity, description length, shrinkage methods, ridge regression, Lasso 
HTF Section 3.3, BIS Sections 1.1, 1.3, 3.1.4, MUR Section 7.5


Th 
Classification Introduction, classification as regression, linear classifiers, risk, conditional risk, logistic regression, MLE, surrogate loss, generalized additive models 
HTF Sections 4.1, 4.4, BIS Sections 1.5, 4.3.2, MUR Sections 8.18.3 

F 
Recitation: Convex Optimization Convex sets, convex function, standard form, Lagrange multipliers, equivalence of constrained and unconstrained versions of ridge regression and Lasso regression 
MRT Appendix B 

T 
Logistic Regression Log odds ratio, logistic function, gradient descent, NewtonRaphson 
BIS Section 4.3.4, SSBD Sections 9.3, 14.1, MUR Section 8.5 

T 
Softmax; stochastic gradient descent Overfitting with logistic regression, MAP estimation, regularization, Softmax, Stochastic gradient descent (SGD) 
BIS Sections 7.1, SSBD Sections 15.115.1.1, MUR Sections 14.5 

F 
Recitation: Matrix cookbook partial derivatives, gradient, linear form, quadratic form, Hessian 


T 
Decision Trees I Partition tree, classification and regression trees (CART), regression tree construction, region splitting, 
BIS Section 14.4 

Th 
Decision Trees II regression tree complexity, regression tree pruning, classification trees, Gini index 
HTF Section 9.2, 9.5 

F 
Recitation: practice midterms



T 
MIDTERM REVIEW 


Th 
MIDTERM



F 
Discuss MIDTERM solutions



Spring Break (3/18  3/22) 

T 
Ensemble methods Combining "weak" classifiers, greedy assembly, AdaBoost algorithm, exponential loss function, weighted loss, optimizing weak learner 
BIS Section 14.3; HTF Sections 10.110.3 

Th 
AdaBoost AdaBoost derivation, AdaBoost behavior, boosting the margin, boosting decision stumps, Boosting and biasvariance tradeoff, combination of regressors, forward stepwise regression, combining regression trees, random forests, classification with random forest, bagging (bootstrap aggregation) 
HTF Sections 10.410.5 

F 
Constrained optimization Constrained optimization problems, Lagrangian, dual function, dual variables, weak duality, strong duality, Slater's condition, KKT conditions, equivalence of constrained and regularized problems 
M14.5 

T 
Support Vector Machines Optimal separating hyperplane, Large margin classifier, margin and regularization, Lagrange multipliers, KKT conditions, maxmargin optimization, quadratic programming, support vectors 
HTF Section 4.5, MRT Sections 4.14.2 

Th 
Support Vector Machines II Nonseparable case, SVMs with slack, loss in SVM, solving SVM in the primal SVM regression 
BIS Section 7.1, SSBD Sections 15.115.1.1, MUR Section 14.5 

F 
Recitation: HW3



T 
Kernel methods solving SVM in the primal, subgradient, subgradient descent, nonlinear features, feature space, kernel trick, representer theorem, kernel SVM in the primal, Mercer's kernels, radial basic function, kernel SVM, SVM regression, multiclass SVMs 
BIS Sections 6.1, 6.2, MRT Sections 5.1, 5.2, 5.3.15.3.2, SSBD Sections 15.2, 15.415.5, MUR Sections 14.12 

Th 
Generative models for classification , generative models, discriminant functions, likelihood ration test, Gaussian discriminant analysis, linear discriminant, quadratic discriminants, generative models for classification, mixture models 
HTF Sections 4.3, 12.412.6 

F 
No recitation/class



T 
Mixture models, the EM algorithm Review multivariate Gaussians, mixture models, likelihood of mixture models, mixture density estimation, expectation maximization, EM for GMM, generic EM for mixture models, EM overfitting and regularization 
HTF Section 12.7; BIS Sections 9.2, 9.3 

Th 
Conditional mixture models Mixture model for regression, mixture of experts model, gating network, conditional mixtures, EM for mixture of experts 
BIS Section 14.5 

F 
Perceptron, Neural Networks Perceptron, perceptron loss, perceptron and neurons, general linear methods  representation as neural networks, twolayer network, feedforward networks, training the networks 
BIS Sections 5.1, 5.2 

T 
No CLASS; recitation: HW4 


Th 
Deep learning Training neural networks, back propagation, MLP as universal approximators, deep vs shallow, non convex optimization, classification networks, multiclass networks, classification networks, multiclass, multilabel, model complexity, learning rate, momemuntum, reLU activation, network ensembles, dropout, multilayer network, network topology, skiplayer connections 
BIS Sections 5.35.5; BIS Section 14.5 

F 
Nonparametric methods, evaluating ML Parametric vs nonparametric methods, nearest neighbor methods, extensions, bias and variance in nearest neighbor methods, locally weighted regression, Classifier evaluation, precisionrecall tradeoff, ROC space, significance of results, significance of crossvalidation 


T 
Representation Learning Unsupervised feature learning, principal component analysis (PCA), power iteration method, kernel PCA, canonical correlation (CCA) 
BIS Sections 12.1, 12.3; HTF Section 14.5 

Th 
Clustering Cluster analysis, dissimilarity based on attributes, kmeans, soft kmeans, hierarchical clustering, spectral clustering 
BIS Section 9.1; HTF Section 14.3 

F 
Learning Theory Probably approximately correct (PAC) learning, finite hypothesis class, infinite hypothesis class, VC dimension, Rademacher complexity, Final Review 
MRT Chapter 2 
