[Statlist] talks on statistics

[Christina Kuenzli]

                  ETH and University of Zurich 

                           Proff. 
         A.D. Barbour - P. Buehlmann - F. Hampel - L. Held
            H.R. Kuensch - M. Maathuis - S. van de Geer

***********************************************************    
           We are glad to announce the following talks
***********************************************************
 
      March 7, 2008   15.15-17.00    LEO C 6

      High Dimensional Sparse Regression and Structure Estimation
      Shuheng Zhou, Carnegie Mellon University, Pittsburgh, PA  

Recent research has demonstrated that sparsity is a powerful technique
in signal reconstruction and in statistical inference. Recent work shows
that l_1-regularized least squares regression can accurately
estimate a sparse model from n noisy samples in p dimensions, even
if p is much larger than n. My work in this area focuses on studying
the role of sparsity in high dimensional regression when the original
noisy samples are compressed, and on structure estimation in Gaussian
graphical models when the graphs evolve over time.

In high-dimensional regression, the sparse object is a vector \beta
in Y = X \beta + \epsilon, where X is n by p matrix such that n <<
p, \beta \in R^{p} and \epsilon \in R^n consists of i.i.d. random
noise. In the classic setting, this problem is ill-imposed for p > n
even for the case when \epsilon =0. However, when the vector \beta
is sparse, one can recover an empirical \hat \beta that is
consistent in terms of its support with true \beta. In joint work
with John Lafferty and Larry Wasserman, we studied the regression
problem under the setting that the original n input variables are
compressed by a random Gaussian ensemble to m examples in p
dimensions, where m << n or p. A primary motivation for this
compression procedure is to anonymize the data and preserve privacy by
revealing little information about the original data. We established
sufficient mutual incoherence conditions on X, under which a sparse
linear model can be successfully recovered from the compressed data.
We characterized the number of random projections that are required
for \ell_1-regularized compressed regression to identify the nonzero
coefficients in the true model with probability approaching one. In
addition, we showed that \ell_1-regularized compressed regression
asymptotically predicts as well as an oracle linear model, a property
called ``persistence''. Finally, we established upper bounds on the
mutual information between the compressed and uncompressed data that
decay to zero.

Undirected graphs are often used to describe high dimensional
distributions.
Under sparsity conditions, the graph can be estimated using \ell_1
penalization methods. However, current methods assume that the data
are independent and identically distributed. If the distribution---and
hence the graph--- evolves over time then the data are no longer
identically distributed. In the second part of the talk, I show how to
estimate the sequence of graphs for non-identically distributed data
and establish some theoretical results. 
This is joint work with John Lafferty and Larry Wasserman.

***********************************************************

      March 7, 2008,     17.15 h    HG  F 30

      Einfuehrungsvorlesung:
      Statistical estimation with censored data

      Marloes Maathuis, Seminar fuer Statistik, ETH Zurich

***********************************************************
       
________________________________________________________
Christina Kuenzli            <kuenzli at stat.math.ethz.ch>
Seminar fuer Statistik      
Leonhardstr. 27,  LEO D11      phone: +41 (0)44 632 3438         
ETH-Zentrum,                   fax  : +41 (0)44 632 1228 
CH-8092 Zurich, Switzerland        http://stat.ethz.ch/~