High-Dimensional Probability Estimation with Deep Density Models

TL;DR

This paper introduces the deep density model (DDM), a novel approach leveraging deep learning to estimate probability densities in high-dimensional data efficiently and explicitly, enabling various probabilistic tasks.

Contribution

The paper presents DDM, a bijective deep learning-based density estimator that allows tractable, explicit density computation and sampling in high-dimensional spaces, addressing limitations of previous models.

Findings

Enables rapid density computation for out-of-sample data

Allows sample generation without MCMC

Facilitates joint entropy estimation

Abstract

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations lie on a lower-dimensional manifold of high probability. It has been more difficult, however, to exploit this insight to build explicit, tractable density models for high-dimensional data. In this paper, we introduce the deep density model (DDM), a new approach to density estimation. We exploit insights from deep learning to construct a bijective map to a representation space, under which the transformation of the distribution of the data is approximately factorized and has identical and known marginal densities. The simplicity of the latent distribution under the model allows us to feasibly explore it, and the invertibility of the map to characterize contraction of measure across it. This enables us to compute normalized densities for out-of-sample data. This combination of tractability and flexibility allows us to tackle a variety of probabilistic tasks on high-dimensional datasets, including: rapid computation of normalized densities at test-time without evaluating a partition function; generation of samples without MCMC; and characterization of the joint entropy of the data.