  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.
