Maximum Entropy Auto-Encoding

TL;DR

This paper introduces a maximum entropy auto-encoder that uses optimal reconstruction for improved performance, demonstrating significant error reduction over conventional auto-encoders, especially in shallow networks.

Contribution

It proposes the deterministic projected belief network (D-PBN) with special non-linearities for optimal reconstruction, extending maximum entropy principles to multi-layer auto-encoders.

Findings

Mean square error reduced by up to 50%.

Performance gains diminish with deeper networks.

Method is most effective with constrained input data.

Abstract

In this paper, it is shown that an auto-encoder using optimal reconstruction significantly outperforms a conventional auto-encoder. Optimal reconstruction uses the conditional mean of the input given the features, under a maximum entropy prior distribution. The optimal reconstruction network, which is called deterministic projected belied network (D-PBN), resembles a standard reconstruction network, but with special non-linearities that mist be iteratively solved. The method, which can be seen as a generalization of maximum entropy image reconstruction, extends to multiple layers. In experiments, mean square reconstruction error reduced by up to a factor of two. The performance improvement diminishes for deeper networks, or for input data with unconstrained values (Gaussian assumption).