[Ml-stat-talks] Fwd: Wilks Statistics Seminar: Bharath Sriperumbudur, Today, April 4th @ 12:30pm, Sherrerd Hall 101
Barbara Engelhardt
bee at princeton.edu
Mon Apr 4 10:13:39 EDT 2016
Talk of interest.
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*** Wilks Statistics Seminar ***
DATE: Today, April 4, 2016
TIME: 12:30pm
LOCATION: Sherrerd Hall 101
SPEAKER: Bharath Sriperumbudur, Pennsylvania State University
TITLE: Density Estimation in Infinite Dimensional Exponential Families
ABSTRACT: We consider an infinite dimensional generalization of natural
exponential family of probability densities, which are parametrized by
functions in a reproducing kernel Hilbert space (RKHS), and show it to be
quite rich in the sense that a broad class of densities on R^d can be
approximated arbitrarily well in Kullback-Leibler (KL) divergence by
elements in the infinite dimensional family, P. Motivated by this
approximation property, we consider the problem of estimating an unknown
density p_0, through an element in P. Standard techniques like maximum
likelihood estimation (MLE) or pseudo MLE (based on the method of sieves),
which are based on minimizing the KL divergence between p_0 and P, do not
yield practically useful estimators because of their inability to
efficiently handle the log-partition function. We propose an estimator
based on minimizing the Fisher divergence between p_0 and P, which involves
solving a simple finite-dimensional linear system. We show the proposed
estimator to be consistent, and provide convergence rates under a
smoothness assumption that log(p_0) belongs to the image of the fractional
power of a Hilbert-Schmidt operator defined on RKHS. Through numerical
simulations we demonstrate that the proposed estimator outperforms the
non-parametric kernel density estimator, and that the advantage of the
proposed estimator grows with increasing dimension.
Joint work with Kenji Fukumizu, Arthur Gretton, Aapo Hyvarinen and Revant
Kumar
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