Nonparametric Density Estimation under Besov IPM Losses

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Abstract

We study the problem of estimating a nonparametric probability distribution under a family of losses called Besov IPMs. This family is quite large, including, for example, \(L^p\) distances, total variation distance, and generalizations of both Wasserstein (earthmover's) and Kolmogorov-Smirnov distances. For a wide variety of settings, we provide both lower and upper bounds, identifying precisely how the choice of loss function and assumptions on the data distribution interact to determine the mini-max optimal convergence rate. We also show that, in many cases, linear distribution estimates, such as the empirical distribution or kernel density estimator, cannot converge at the optimal rate. These bounds generalize, unify, or improve on several recent and classical results. Moreover, IPMs can be used to formalize a statistical model of generative adversarial networks (GANs). Thus, we show how our results imply bounds on the statistical error of a GAN, showing, for example, that, in many cases, GANs can strictly outperform the best linear estimator.

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druGAN: An Advanced Generative Adversarial Autoencoder Model for de Novo Generation of New Molecules with Desired Molecular Properties in Silico.

Artur Kadurin, Sergey Nikolenko, Kuzma Khrabrov … (2017)

Deep generative adversarial networks (GANs) are the emerging technology in drug discovery and biomarker development. In our recent work, we demonstrated a proof-of-concept of implementing deep generative adversarial autoencoder (AAE) to identify new molecular fingerprints with predefined anticancer properties. Another popular generative model is the variational autoencoder (VAE), which is based on deep neural architectures. In this work, we developed an advanced AAE model for molecular feature extraction problems, and demonstrated its advantages compared to VAE in terms of (a) adjustability in generating molecular fingerprints; (b) capacity of processing very large molecular data sets; and (c) efficiency in unsupervised pretraining for regression model. Our results suggest that the proposed AAE model significantly enhances the capacity and efficiency of development of the new molecules with specific anticancer properties using the deep generative models.