CS274A, Spring 2008: Probabilistic Learning

  CompSci   274A     PROB LEARNING
CodeTypSecUntInstructorTimePlaceFinal
35300LecA4IHLER, A.TuTh   2:00- 3:20pSSL 206Thu, Jun 12, 1:30-3:30pm


Introduction to probabilistic models, inference, and learning.

CS274A is an introductory course to probabilistic approaches to learning from data. Probabilistic models form an important part of many areas of computer science, and probabilistic learning (in this context, automatically constructing probabilistic models from data) has become an important tool in sub-fields such as artificial intelligence, data mining, speech recognition, computer vision, bioinformatics, signal processing, and many more. CS274A will provide an introduction to the concepts and principles which underly probabilistic models, and apply these principles to the development, analysis, and practical application of machine learning algorithms.

The course will focus primarily on parametric probabilistic modeling, including data likelihood, parameter estimation using likelihood and Bayesian approaches, hypothesis testing and classification problems, density estimation, clustering, and regression. Related problems, including model selection, overfitting, and bias/variance trade-offs will also be discussed.

Background. The course is intended to be an introduction to probabilistic learning, and thus has few explicit requirements. Students are expected to be familiar with basic concepts from probability, linear algebra, multivariate calculus, etc. Homeworks will use the MATLAB programming environment, but no prior experience with MATLAB is required for the course.

From the course catalog: Probabilistic Learning: Theory and Algorithms. An introduction to probabilistic and statistical techniques for learning from data, including parameter estimation, density estimation, regression, classification, and mixture modeling.

Course format. Two lectures per week. Homeworks due approximately every two weeks. Two exams (midterm and final). Grading: 40% homework, 30% midterm, 30% final.

Textbooks. The required textbook for the course is Bishop's "Pattern Recognition and Machine Learning", but lectures are likely to follow the book only loosly. Other recommended reading include MacKay's "Information Theory, Inference, and Learning Algorithms" (available online at http://www.inference.phy.cam.ac.uk/mackay/itila/), Duda, Hart, and Stork's "Pattern Classification", and Hastie, Tibshirani, and Friedman's "Elements of Statistical Learning".

(Tentative) Schedule of Topics.

Week 1

04/01/2008

Introduction; probability distributions, Bayes' rule, etc.

 

    

 

04/03/2008

introduction continued; multivariate distributions

 

    


Week 2

04/07/2008

Intro to learning. Parameters, likelihood functions. Bias/Variance.

 

    

 

04/09/2008

Maximum likelihood learning I: univariate exponential family

 

    


Week 3

04/14/2008

Maximum likelihood learning II: multivariate models

 

    

 

04/16/2008

Bayesian learning I: prior and posterior distributions; MAP estimation

 

    


Week 4

04/21/2008

Bayesian learning II: conjugate prior distributions

 

    

 

04/23/2008

Bayesian learning III: Bayesian estimation; Monte Carlo methods

 

    


Week 5

04/28/2008

Regression I: linear and logistic regression

 

    

 

04/30/2008

MIDTERM EXAM

 

    


Week 6

05/06/2008

Regression II: probabilistic interpretations, parameter estimation

 

    

 

05/08/2008

Classification I: introduction, risk, optimality; hypothesis testing

 

    


Week 7

05/13/2008

Classification II: discriminants and classification boundaries

 

    

 

05/15/2008

Classification III: linear classifiers; connections to regression

 

    


Week 8

05/20/2008

Mixture models and EM: mixtures of Gaussians; k-means; EM

 

    

 

05/22/2008

Mixture models and EM: more on expectation-maximization

 

    


Week 9

05/27/2008

Graphical models I: structured multivariate distributions

 

    

 

05/29/2008

Graphical models II: using structure for efficient computation; Kalman filtering, forward-backward

 

    


Week 10

06/03/2008

Additional topics: TBD

 

    

 

06/05/2008

Additional topics: TBD

 

    


Final Exam

06/12/2008

In class final exam, 1:30-3:30pm