Easy Variational Inference for Categorical Models via an Independent Binary Approximation

We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. GLMs have been difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using conjugate auxiliary variable methods. We define a new class of GLMs for categorical data called categorical-from-binary (CB) models. Each CB model has a likelihood that is bounded by the product of binary likelihoods, suggesting a natural posterior approximation. This approximation makes inference straight-forward and fast; using well-known auxiliary variables for probit or logistic regression, the product of binary models admits conjugate closedform variational inference that is embarrassingly parallel across categories and invariant to category ordering. Moreover, an independent binary model simultaneously approximates multiple CB models. Bayesian model averaging over these can improve the quality of the approximation for any given dataset. We show that our approach scales to thousands of categories, outperforming posterior estimation competitors like Automatic Differentiation Variational Inference (ADVI) and No U-Turn Sampling (NUTS) in the time required to achieve fixed prediction quality.

Automated summary

This paper presents a new class of generalized linear models (GLMs) for categorical data and proposes a posterior approximation method based on binary categorical-from-binary (CB) models, which allows for fast and simple inference. The quality of the approximation can be improved through Bayesian model averaging. Experimental results show that this method outperforms other posterior estimation methods in dealing with a large number of categories.