MADE: Masked Autoencoder for Distribution Estimation

TL;DR

MADE introduces a masked autoencoder framework that efficiently estimates complex probability distributions by respecting autoregressive constraints, enabling fast, scalable, and competitive generative modeling across various architectures.

Contribution

It proposes a simple masking technique for autoencoders to model distributions autoregressively, allowing flexible, fast, and scalable generative modeling with multiple orderings.

Findings

Competitive with state-of-the-art estimators

Faster and more scalable at test time

Applicable to various neural network architectures

Abstract

There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the autoencoder's parameters to respect autoregressive constraints: each input is reconstructed only from previous inputs in a given ordering. Constrained this way, the autoencoder outputs can be interpreted as a set of conditional probabilities, and their product, the full joint probability. We can also train a single network that can decompose the joint probability in multiple different orderings. Our simple framework can be applied to multiple architectures, including deep ones. Vectorized implementations, such as on GPUs, are simple and fast. Experiments demonstrate that this approach is competitive with state-of-the-art tractable distribution estimators. At test time, the method is significantly faster and scales better than other autoregressive estimators.