Jing Lei

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This is the web page of 36-785 in Spring 2012. It is being updated constantly. Please check frequently for updates.

Course title: Hidden Markov and State Space Models

Instructor: Jing Lei, office: 229G BH, jinglei [at] andrew [dot] cmu [dot] edu

Office Hours: Wednesdays 2:30-3:30

Lecture time and location: WMF 1:30-2:20, WEH 5312.

TA: Jionglin Wu (jionglin [at] andrew [dot] cmu [dot] edu), Office hours: Friday 11-12 in the statistics tutoring room in FMS.

Course description:

Hidden Markov and state space models are powerful modeling and prediction tools for sequential data observed from dynamic systems. This mini course will introduce some basic concepts and examples in this area. We will talk about the algorithm, theory, and applications in a variety of related topics, including ARMA models, Kalman filters, particle filters, filtering and prediction using sequential Monte Carlo methods.

Prerequisites First-year graduate courses in probability and statistics. Part of the course will require familiarity with statistical computing packages such as Matlab or R.

Recommended readings

  1. Inference in Hidden Markov Models, by Olivier Cappe, Eric Moulines, and Tobias Ryden. 2005, Springer. Free pdf access using CMU library VPN.
  2. Time Series Analysis and Its Applications, by Robert Shumway and David Stoffer (3rd Ed.), 2011, Springer. Free pdf access using CMU library VPN.
More references can be found on M. Jordan's course website.

Syllabus: A pdf file of the syllabus.

Outline

  1. Week of Jan 16: Motivating examples. Basic concepts of Markov chains and HMM. Notes updated: 2012-01-25 11:05 pm
  2. Week of Jan 23: HMM in discrete state spaces. Baum-Welch algorithm, Viterbi algorithm. Notes updated: 2012-01-25 11:05 pm
  3. Week of Jan 30: HMM in continuous state spaces. I: Gaussian models and Kalman filters. Application in numerical weather forecasting. Notes updated: 2012-02-10 11:05 am
  4. Week of Feb 6: HMM in continuous state space. II: particle filters and sequential Monte Carlo methods. Notes updated: 2012-02-17 3:05 pm
  5. Week of Feb 13: Recursive filtering and theory of particle filters.
  6. Week of Feb 20: Parameter estimation and model selection in HMM. Notes updated: 2012-03-01 9:53 pm
  7. Week of Feb 27 and Mar 5: Parameter estimation for Gaussian linear models. Monte Carlo based EM algorithm. Notes updated: 2012-03-05 4:40 pm

Lecture notes

Lecture notes will be posted here before or soon after each lecture.

Homeworks

There will be a few (2-3) homework assignments. Part of the homework will be to complete some partial arguments omitted in the main lecture or to derive some useful auxiliary results. Part of the homework will involve programming in Matlab or R to implement the algorithms in real world or synthetic data sets.
Homework #1 updated: 2012-01-25 11:05 pm Solutions, R code
Homework #2 updated: 2012-02-13 2:43 pm Solutions, R code
Homework #3 updated: 2012-02-20 12:53 pm R code provided by Li Liu.