Publisher = {JMLR Workshop and Conference Proceedings},

Title = {Nonparametric Estimation of Renyi Divergence and Friends},

Url = {http://jmlr.org/proceedings/papers/v32/krishnamurthy14.pdf},

Abstract = {We consider nonparametric estimation of $L_2$, Renyi-$\alpha$ and Tsallis-$\alpha$ divergences between continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them into divergence estimators. For the integral functionals, our estimators are based on corrections of a preliminary plug-in estimator. We show that these estimators achieve the parametric convergence rate of $n^{-1/2}$ when the densities' smoothness, $s$, are both at least $d/4$ where $d$ is the dimension. We also derive minimax lower bounds for this problem which confirm that $s > d/4$ is necessary to achieve the $n^{-1/2}$ rate of convergence. We validate our theoretical guarantees with a number of simulations.},

Author = {Akshay Krishnamurthy and Kirthevasan Kandasamy and Barnabas Poczos and Larry Wasserman},

Editor = {Tony Jebara and Eric P. Xing},

Year = {2014},

Booktitle = {Proceedings of the 31st International Conference on Machine Learning (ICML-14)},

Pages = {919-927}

}