The course combines methodology with theoretical foundations and computational aspects. It treats both the "art" of designing good learning algorithms and the "science" of analyzing an algorithm's statistical properties and performance guarantees. Theorems are presented together with practical aspects of methodology and intuition to help students develop tools for selecting appropriate methods and approaches to problems in their own research.

The course includes topics in statistical theory that are now becoming important for researchers in machine learning, including consistency, minimax estimation, and concentration of measure. It also presents topics in computation including elements of convex optimization, variational methods, randomized projection algorithms, and techniques for handling large data sets.

Topics will be chosen from the following basic outline, which is subject to change.

• Statistical theory: Maximum likelihood, Bayes, minimax, Parametric versus Nonparametric Methods, Bayesian versus Non-Bayesian Approaches, classification, regression, density estimation.
• Convexity and optimization: Convexity, conjugate functions, unconstrained and constrained optimization, KKT conditions.
• Parametric methods: Linear Regression, Model Selection, Generalized Linear Models, Mixture Models, Classification (linear, logistic, support vector machines), Graphical Models, Structured Prediction, Hidden Markov Models.
• Sparsity: High Dimensional Data and Sparsity, Basis Pursuit and the Lasso Revisited, Sparsistency, Consistency, Persistency, Greedy Algorithms for Sparse Linear Regression, Sparsity in Nonparametric Regression. Sparsity in Graphical Models, Compressed Sensing.
• Nonparametric methods: Nonparametric Regression and Density Estimation, Nonparametric Classification, Boosting, Clustering and Dimension Reduction, PCA, Manifold Methods, Principal Curves, Spectral Methods, The Bootstrap and Subsampling, Nonparametric Bayes.
• Advanced theory: Concentration of Measure, Covering numbers, Learning theory, Risk Minimization, Tsybakov noise, minimax rates for classification and regression, surrogate loss functions, boosting, sparsistency, Minimax theory.
• Kernel methods: Mercel kernels, reproducing kernel Hilbert spaces, relationship to nonparametric statistics, kernel classification, kernel PCA, kernel tests of independence.
• Computation: The EM Algorithm, Simulation, Variational Methods, Regularization Path Algorithms, Graph Algorithms.
• Other learning methods: Functional Data, Semi-Supervised Learning, Reinforcement Learning, Minimum Description Length, Online Learning, The PAC Model, Active Learning.