[Ml-stat-talks] Fwd: Seminar

Barbara Engelhardt bee at princeton.edu
Tue Jul 19 11:51:13 EDT 2016


Talk of interest tomorrow.

The date is July 20 (tomorrow) and the time is 4:30pm, the location is
Sherrerd Hall 101.




              *DEPARTMENTS OF*
*ELECTRICAL ENGINEERING*
*and*
*OPERATIONS RESEARCH AND*
*FINANCIAL ENGINEERING*
              *SEMINAR*



*Speaker:      Esa Ollila*
Aalto University
*Title:             Simultaneous penalized M-estimation of covariance
matrices and an application to regularized discriminant analysis*
*Date:             Wednesday, July 20, 2016          *
*Time:             *4:30 pm
*Room:           *Sherrerd Hall, Room 101
*Host:             Vincent Poor and Han Liu*

*Abstract:  *A common assumption when sampling p-dimensional observations
from K distinct group is the equality of the covariance matrices.  In this
paper, we propose two penalized M-estimation approaches for the estimation
of the covariance or scatter matrices under the broader assumption that
they may simply be close to each other, and hence roughly deviate from some
positive definite “center''.  The first approach begins by generating a
pooled M-estimator of scatter based on all the data, followed by a
penalised M-estimator of scatter for each group, with the penalty term
chosen so that the individual scatter matrices are shrunk towards the
pooled scatter matrix. In the second approach, we minimize the sum of the
individual group M-estimation cost functions together with an additive
joint penalty term which enforces some similarity between the individual
scatter estimators, i.e. shrinkage towards a mutual center.  In both
approaches, we utilize the concept of geodesic convexity to prove the
existence and uniqueness of the penalized solution under general
conditions.  We consider three specific penalty functions based on the
Euclidean, the Riemannian, and the Kullback-Leibler distances. In the
second approach, the distance based penalties are shown to lead to
estimators of the mutual center that are related to the arithmetic, the
Riemannian and the harmonic means of positive definite matrices,
respectively. A penalty based on an ellipticity measure is also considered
which is particularly useful for shape matrix estimators. Fixed point
equations are derived for each penalty function and the benefits of the
estimators are illustrated in regularized discriminant analysis problem.

This is joint work with Ilya Soloveychik, David E. Tyler and  Ami Wiesel.

*B**io**: *Esa Ollila received the M.Sc. degree in mathematics from the
University of Oulu, in 1998, Ph.D. degree in statistics with honors from
the University of Jyvaskyla, in 2002, and the D.Sc. (Tech) degree with
honors in signal processing from Aalto University, in 2010. From 2004 to
2007 he was a post-doctoral fellow and from August 2010 to May 2015 an
Academy Research Fellow of the Academy of Finland. He has also been a
Senior Lecturer at the University of Oulu. Currently, he is an Associate
Professor of Signal Processing at Aalto University. He is also an adjunct
Professor (statistics) of Oulu University. Fall-term 2001 he was a Visiting
Researcher with the Department of Statistics, Pennsylvania State
University, while the academic year 2010-2011 he spent as a Visiting
Post-doctoral Research Associate with the Department of Electrical
Engineering, Princeton University.  He is a member of EURASIP SAT in
Theoretical and Methodological Trends in Signal Processing (TMTSP). His
research interests contain multivariate analysis and robust statistics,
statistical learning, radar and array signal processing and statistical
signal processing at large.
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