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 and the development of theoretical concepts to support such methods.


  • Kernel methods---basic algorithms
    Classification and regression
    Lagrangian duality
    Mercer's theorem
    String kernels, convolutional kernels
    Kernel discriminant analysis, kernel logistic regression
    Kernel PCA, kernel CCA, kernel ICA
  • Kernel methods---basic theory
    Reproducing kernel Hilbert spaces
    Representer theorem
    Regularization operators
    Gaussian processes
  • Spectral methods
    Spectral graph partitioning
    Spectral clustering
  • Ensemble methods
    Bagging, boosting
    Convex loss functions
  • Parametric Bayesian models
    Hierarchical models, empirical Bayes
    Gibbs sampling
    Conjugate duality, variational inference
  • Nonparametric Bayesian methods
    Dirichlet process, Chinese restaurant process, stick-breaking priors
    Dirichlet process mixtures
    Hierarchical Dirichlet processes
  • Risk bounds
    Glivenko-Cantelli classes and Rademacher averages
    Growth functions and VC dimension
    Covering numbers
  • Model selection methods
    Cross validation
    Bayesian methods