Neural Autoregressive Distribution Estimation

TL;DR

NADE models are neural network architectures for unsupervised density estimation that leverage autoregressive decomposition, weight sharing, and convolutional structures to achieve tractable and effective modeling of binary and real-valued data.

Contribution

Introduction of NADE models that combine autoregressive factorization with neural networks, including deep and convolutional variants, for improved density estimation.

Findings

NADE achieves competitive density estimation performance.

Deep NADE models can be trained to be order-agnostic.

Convolutional NADE exploits image pixel structure effectively.

Abstract

We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discuss how they achieve competitive performance in modeling both binary and real-valued observations. We also present how deep NADE models can be trained to be agnostic to the ordering of input dimensions used by the autoregressive product rule decomposition. Finally, we also show how to exploit the topological structure of pixels in images using a deep convolutional architecture for NADE.