A Deep and Tractable Density Estimator

TL;DR

This paper introduces a scalable deep NADE model trained across all variable orderings, enabling flexible inference and achieving state-of-the-art density estimation results.

Contribution

It presents a novel training method for deep NADE models that share parameters across all variable orderings, improving scalability and inference flexibility.

Findings

Ensembles of Deep NADE achieve state-of-the-art density estimation.

The training procedure scales to deep models.

Flexible inference tasks are facilitated by multiple orderings.

Abstract

The Neural Autoregressive Distribution Estimator (NADE) and its real-valued version RNADE are competitive density models of multidimensional data across a variety of domains. These models use a fixed, arbitrary ordering of the data dimensions. One can easily condition on variables at the beginning of the ordering, and marginalize out variables at the end of the ordering, however other inference tasks require approximate inference. In this work we introduce an efficient procedure to simultaneously train a NADE model for each possible ordering of the variables, by sharing parameters across all these models. We can thus use the most convenient model for each inference task at hand, and ensembles of such models with different orderings are immediately available. Moreover, unlike the original NADE, our training procedure scales to deep models. Empirically, ensembles of Deep NADE models obtain state of the art density estimation performance.