[Colloquium] Reminder: Wang/MS Presentation/May 22, 2015

[Margaret Jaffey]

This is a reminder about Jialei's MS Presentation tomorrow.

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Date:  Friday, May 22, 2015

Time:  1:00 PM

Place:  Ryerson 277

M.S. Candidate:  Jialei Wang

M.S. Paper Title: Inference for Sparse Conditional Precision Matrices

Abstract:
Given n i.i.d. observations of a random vector (X,Z), where X is a
high-dimensional vector and Z is a low-dimensional index variable, we
study the problem of estimating the conditional inverse covariance
matrix
Ω(z)=(E[(X−E[X∣Z])(X−E[X∣Z])^T|Z=z])^{−1}
under the assumption that the set of non-zero elements is small and
does not depend on the index variable. We develop a novel procedure
that combines the ideas of the local constant smoothing and the group
Lasso for estimating the conditional inverse covariance matrix. A
proximal iterative smoothing algorithm is used to solve the
corresponding convex optimization problems. We prove that our
procedure recovers the conditional independence assumptions of the
distribution X∣Z with high probability. This result is
established by developing a uniform deviation bound for the
high-dimensional conditional covariance matrix from its population
counterpart, which may be of independent interest. Furthermore, we
develop point-wise confidence intervals for individual elements of the
conditional inverse covariance matrix. We perform extensive simulation
studies, in which we demonstrate that our proposed procedure
outperforms sensible competitors. We illustrate our proposal on a S&P
500 stock price data set.

Jialei's advisors are Prof. John Lafferty and Prof. Mladen Kolar

Login to the Computer Science Department website for details:
 https://www.cs.uchicago.edu/phd/ms_announcements#jialei

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Margaret P. Jaffey            margaret at cs.uchicago.edu
Department of Computer Science
Student Support Rep (Ry 156)               (773) 702-6011
The University of Chicago      http://www.cs.uchicago.edu
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