[Colloquium] Research at TTIC: Xiaohui Chen

[Liv Leader]

When:     Friday, March 2 @ Noon

Where:   TTIC Conference Room #530, 6045 S. Kenwood Avenue, 5th Floor

Who:      Xiaohui Chen

Title:     Statistical Estimation of High-Dimensional Sparse Precision
Matrices

Abstract:

Abstract: Estimation of high-dimensional inverse covariance matrix (a.k.a.
precision matrix) is of great importance in a broad range of statistical
machine learning problems and it has many open challenges. In this talk, I
will discuss two aspects of this problem from the computational and
theoretic perspectives.

In the first part, we will describe an easy-to-implement and
computationally efficient algorithm for estimating large precision matrix.
The domain of this estimator is an explicitly constructed class of
approximately inversely closed sparse matrices. Our estimator is not based
on optimization and thus it differs in nature from most state-of-the-art
sparse precision matrix estimation methods. Various theoretical performance
bounds of the proposed estimator will be given and it is shown to be
optimal in the sense of minimax under the spectral risk.

In the second part, we will discuss estimation issues, in particular under
the graphical Lasso setting, for time-varying precision matrix based on
limited observations generated from multiple casual stochastic processes.
Estimation under dependence and high-dimensionality is notoriously
difficult and largely remains unknown. We will show that, under mild
conditions, kernel smoothed version of the graphical Lasso estimator is
consistent under the Frobenius norm. Our analysis framework is broad enough
to allow not only the parameters evolving over time; but also the bona fide
dependence structures on the measurement errors. Applications to locally
stationary times-series and linear processes are given.

Time permitting, generalization of our results to functional versions will
be briefly discussed.


*****

Research at TTIC Seminar Series

TTIC is hosting a weekly seminar series presenting the research currently
underway at the Institute. Every week a different TTIC faculty member will
present their research.  The lectures are intended both for students
seeking research topics and adviser, and for the general TTIC and
University of Chicago communities interested in hearing what their
colleagues are up to.

To receive announcements about the seminar series, please subscribe to the
mailing list: https://groups.google.com/a/ttic.edu/group/talks/subscribe

Speaker details can be found at: http://www.ttic.edu/tticseminar.php.

For additional questions, please contact Nati Srebro at nati at ttic.edu.

-- 
Liv Leader
Human Resources Coordinator

Toyota Technological Institute Chicago
6045 S Kenwood Ave
Chicago, IL 60637
Phone- (773) 702-5033
Fax-     (773) 834-9881
Email-  lleader at ttic.edu <jam at ttic.edu>
Web-   www.ttic.edu
<http://www.ttic.edu/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mailman.cs.uchicago.edu/pipermail/colloquium/attachments/20120229/b392ab64/attachment-0001.htm