Generalized Denoising Auto-Encoders as Generative Models
This addresses a theoretical gap in generative modeling for machine learning researchers, but appears incremental as it builds on existing auto-encoder frameworks.
The paper tackles the problem of connecting regularized auto-encoders to implicit density estimation for discrete or continuous data with arbitrary corruption and reconstruction losses, removing biases from non-infinitesimal noise. It proposes a new approach that generalizes denoising auto-encoders to handle these issues without specifying concrete results or numbers.
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).