Generalized Denoising Auto-Encoders as Generative Models

TL;DR

This paper extends denoising auto-encoders to serve as flexible generative models capable of handling discrete and continuous data, arbitrary corruption, and non-infinitesimal noise, with improved theoretical justification.

Contribution

It introduces a unified framework for generalized denoising auto-encoders that can model complex data distributions beyond Gaussian noise and small corruption assumptions.

Findings

Applicable to discrete and continuous data

Handles arbitrary corruption and reconstruction loss

Removes bias from non-infinitesimal noise

Abstract

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).