Nearest neighbor density functional estimation based on inverse Laplace transform

A general approach to $L_2$-consistent estimation of various density functionals using $k$-nearest neighbor distances is proposed, along with the analysis of convergence rates in mean squared error. The construction of the estimator is based on inverse Laplace transforms related to the target density functional, which arises naturally from the convergence of a normalized volume of $k$-nearest neighbor ball to a Gamma distribution in the sample limit. Some instantiations of the proposed estimator rediscover existing $k$-nearest neighbor based estimators of Shannon and Renyi entropies and Kullback--Leibler and Renyi divergences, and discover new consistent estimators for many other functionals, such as Jensen--Shannon divergence and generalized entropies and divergences. A unified finite-sample analysis of the proposed estimator is presented that builds on a recent result by Gao, Oh, and Viswanath (2017) on the finite sample behavior of the Kozachenko--Leoneko estimator of entropy.

Energy-Based Sequence GANs for Recommendation and Their Connection to Imitation Learning

Recommender systems aim to find an accurate and efficient mapping from historic data of user-preferred items to a new item that is to be liked by a user. Towards this goal, energy-based sequence generative adversarial nets (EB-SeqGANs) are adopted for recommendation by learning a generative model for the time series of user-preferred items. By recasting the energy function as the feature function, the proposed EB-SeqGANs is interpreted as an instance of maximum-entropy imitation learning.