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 and the development
of theoretical concepts to support such methods.
Outline:
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- 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
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- Kernel methods---basic theory
- Reproducing kernel Hilbert spaces
- Representer theorem
- Regularization operators
- Gaussian processes
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- Spectral methods
- Spectral graph partitioning
- Spectral clustering
- Relaxations
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- Ensemble methods
- Bagging, boosting
- Convex loss functions
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- Parametric Bayesian models
- Hierarchical models, empirical Bayes
- Gibbs sampling
- Metropolis-Hastings
- Conjugate duality, variational inference
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- Nonparametric Bayesian methods
- Dirichlet process, Chinese restaurant process, stick-breaking priors
- Dirichlet process mixtures
- Hierarchical Dirichlet processes
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- Risk bounds
- Glivenko-Cantelli classes and Rademacher averages
- Growth functions and VC dimension
- Covering numbers
- Convexity
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- Model selection methods
- Cross validation
- TIC
- MDL/BIC
- Bayesian methods