printer friendly pageSTATS 306B: Methods for Applied Statistics: Unsupervised Learning
Unsupervised learning techniques in statistics, machine learning, and data mining.
Terms: Spr
| Units: 2-3
Instructors:
Mackey, L. (PI)
STATS 310A: Theory of Probability (MATH 230A)
Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites: 116,
MATH 171.
Terms: Aut
| Units: 2-4
Instructors:
Diaconis, P. (PI)
STATS 310B: Theory of Probability (MATH 230B)
Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,nn(v) ergodic theory. Prerequisite: 310A or
MATH 230A.
Terms: Win
| Units: 2-3
Instructors:
Montanari, A. (PI)
STATS 310C: Theory of Probability (MATH 230C)
Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or
MATH 230B.
Terms: Spr
| Units: 2-4
Instructors:
Chatterjee, S. (PI)
STATS 313: Introduction to Graphical Models (STATS 213)
Multivariate Normal Distribution and Inference, Wishart distributions, graph theory, probabilistic Markov models, pairwise and global Markov property, decomposable graph, Markov equivalence, MLE for DAG models and undirected graphical models, Bayesian inference for DAG models and undirected graphical models. Prerequisites:
STATS 116 (preferably
STATS 217),
STATS 200 (preferably
STATS 300A),
MATH 104 or equivalent class in linear algebra.
Terms: Win
| Units: 3
Instructors:
Rajaratnam, B. (PI)
STATS 314: Advanced Statistical Methods
Topic this year is empirical likelihood. Empirical likelihood (EL) allows likelihood based inferences without assuming any parametric form for the likelihood. It is based instead on reweighting the sample values. It provides data driven shapes for confidence regions and confidence bands. EL tests have competitive power.nnThis course covers: nonparametric maximum likelihood and likelihood ratios, censoring and truncation, biased sampling, estimating equations, GMM, Bayesian bootstrap, Euclidean and Kullback-Leibler log likelihoods and recentnnresearch directions.
Terms: Aut
| Units: 3
| Repeatable
for credit
Instructors:
Owen, A. (PI)
STATS 315A: Modern Applied Statistics: Learning
Overview of supervised learning. Linear regression and related methods. Model selection, least angle regression and the lasso, stepwise methods. Classification. Linear discriminant analysis, logistic regression, and support vector machines (SVMs). Basis expansions, splines and regularization. Kernel methods. Generalized additive models. Kernel smoothing. Gaussian mixtures and the EM algorithm. Model assessment and selection: crossvalidation and the bootstrap. Pathwise coordinate descent. Sparse graphical models. Prerequisites:
STATS 305, 306A,B or consent of instructor.
Terms: Win
| Units: 2-3
Instructors:
Hastie, T. (PI)
STATS 315B: Modern Applied Statistics: Data Mining
Two-part sequence. New techniques for predictive and descriptive learning using ideas that bridge gaps among statistics, computer science, and artificial intelligence. Emphasis is on statistical aspects of their application and integration with more standard statistical methodology. Predictive learning refers to estimating models from data with the goal of predicting future outcomes, in particular, regression and classification models. Descriptive learning is used to discover general patterns and relationships in data without a predictive goal, viewed from a statistical perspective as computer automated exploratory analysis of large complex data sets.
Terms: Spr
| Units: 2-3
Instructors:
Friedman, J. (PI)
STATS 317: Stochastic Processes
Semimartingales, stochastic integration, Ito's formula, Girsanov's theorem. Gaussian and related processes. Stationary/isotropic processes. Integral geometry and geometric probability. Maxima of random fields and applications to spatial statistics and imaging.
Terms: Spr
| Units: 3
STATS 319: Literature of Statistics
Literature study of topics in statistics and probability culminating in oral and written reports. May be repeated for credit.
Terms: Aut, Win, Spr
| Units: 1-3
| Repeatable
for credit
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