Deep Energy Estimator Networks

TL;DR

This paper introduces Deep Energy Estimator Networks (DEEN), a scalable, inference-free framework for density estimation in high-dimensional data using score matching and neural networks.

Contribution

It presents a novel deep energy estimator network that effectively learns unnormalized densities and scores without inference, addressing stability issues in high-dimensional settings.

Findings

DEEN successfully learns energy functions for synthetic and high-dimensional data.

The method enables effective single-step denoising.

It diagnoses and addresses stability problems in score estimation.

Abstract

Density estimation is a fundamental problem in statistical learning. This problem is especially challenging for complex high-dimensional data due to the curse of dimensionality. A promising solution to this problem is given here in an inference-free hierarchical framework that is built on score matching. We revisit the Bayesian interpretation of the score function and the Parzen score matching, and construct a multilayer perceptron with a scalable objective for learning the energy (i.e. the unnormalized log-density), which is then optimized with stochastic gradient descent. In addition, the resulting deep energy estimator network (DEEN) is designed as products of experts. We present the utility of DEEN in learning the energy, the score function, and in single-step denoising experiments for synthetic and high-dimensional data. We also diagnose stability problems in the direct estimation of the score function that had been observed for denoising autoencoders.