Augment and Reduce: Stochastic Inference for Large Categorical Distributions

TL;DR

This paper introduces Augment and Reduce (A&R), a general stochastic inference method that reduces computational costs for large categorical distributions in machine learning, improving efficiency and predictive accuracy.

Contribution

A&R combines latent variable augmentation with stochastic variational inference, offering a more general approach than softmax-specific methods for large categorical models.

Findings

A&R provides a tighter bound on marginal likelihood.

A&R achieves better predictive performance.

A&R scales efficiently to large outcome spaces.

Abstract

Categorical distributions are ubiquitous in machine learning, e.g., in classification, language models, and recommendation systems. However, when the number of possible outcomes is very large, using categorical distributions becomes computationally expensive, as the complexity scales linearly with the number of outcomes. To address this problem, we propose augment and reduce (A&R), a method to alleviate the computational complexity. A&R uses two ideas: latent variable augmentation and stochastic variational inference. It maximizes a lower bound on the marginal likelihood of the data. Unlike existing methods which are specific to softmax, A&R is more general and is amenable to other categorical models, such as multinomial probit. On several large-scale classification problems, we show that A&R provides a tighter bound on the marginal likelihood and has better predictive performance than existing approaches.