Syllabus

Course Description:

This course will provide an introduction to advanced statistical and computational methods for the modeling of complex, multivariate data. The focus will be on nonparametric methods, the development of theoretical concepts to support such methods, and tools for model selection and model averaging.

Outline:

Model selection and model averaging Tree models Markov random fields Cross validation TIC MDL/BIC Bayesian methods: Tree models; Markov random fields; Cross validation; TIC; MDL/BIC; Bayesian methods

Kernel methods---basic theory Reproducing kernel Hilbert spaces Representer theorem Regularization operators Gaussian processes Dot product kernels Conditionally positive definite kernels: Reproducing kernel Hilbert spaces; Representer theorem; Regularization operators; Gaussian processes; Dot product kernels; Conditionally positive definite kernels

Kernel methods---applications Support vector classification Support vector regression One class support vector machine Kernel PCA Kernel discriminant analysis: Support vector classification; Support vector regression; One class support vector machine; Kernel PCA; Kernel discriminant analysis

Capacity concepts Annealed entropy Growth functions and VC dimension Applications to uniform convergence bounds: Annealed entropy; Growth functions and VC dimension; Applications to uniform convergence bounds

Ensemble methods Bagging Boosting: Bagging; Boosting