M39

XuanLong Nguyen, Martin Wainwright and Michael Jordan

Estimating divergence functionals and the likeliho o d ratio by p enalized convex risk minimization ˇ given n resp. m i.i.d. samples: X1 , . . . Xn Y1 , . . . Ym   P (unknown) Q (unknown)

ˇ propose, analyze and evaluate convergence behavior of a nonparametric estimator for divergence functional D (P, Q) based on (X, Y ): D (P, Q) :=  d Q dP d P=  q
0

p0
dP dQ

p

0 dľ.

­ also estimator of likelihood ratio function

ˇ applications: estimating mutual information and KL divergence in coding, independent component analysis, dimensionality reduction, experiment design,... ˇ idea: based on variational characterization of divergence functionals