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Summer Course on High Dimensional Statistical Inference

Instructor

Tony Cai, Dorothy Silberberg Professor of Statistics at the Wharton School of the University of Pennsylvania
Email: tcai@wharton.upenn.edu
Web: http://stat.wharton.upenn.edu/~tcai/Biosketch.html

Ming Yuan, Professor, Department of Statistics, University of Wisconsin-Madison
Email: myuan@stat.wisc.edu
Web: http://www.stat.wisc.edu/~myuan/Site/Welcome.html

Basic Information

Credit:2
Credit Hour:32
Time:14:00-17:40, July 8, July 10, July 12; 08:00-11:40, July 9, July 11, July 13 (Week 20)
Classroom:Room 601, Zhiyuan College, Pao Yue-Kong Library, SJTU
Course Code:MA346

Outline

This course will cover high-dimensional statistical inference with the focus on the recovery of high dimensional sparse signals and the estimation of large matrices. These and other related problems have attracted much recent interest in a range of fields including statistics, applied mathematics and electrical engineering. We will discuss in detail the penalized and constrainedl1minimization methods and give a unified and elementary analysis on sparse signal recovery in three settings: noiseless, bounded noise and Gaussian noise. This course will also present the latest results on optimal estimation of large covariance/precision matrices. More specially, the course will cover the following topics:

  1. Compressed sensing: recovery of sparse signals in the noiseless case;
  2. High-dimensional linear regression: LASSO, Dantzig Selector;
  3. Construction of compressed sensing matrices;
  4. Estimation of general matrices;
  5. Estimation of covariance matrices;
  6. Estimation of precision matrices.

Time permitting, high dimensional linear discriminant analysis will also be discussed at the end.