Kullback-Leibler Proximal Variational Inference

We propose a new variational inference method based on a proximal framework that uses the Kullback-Leibler (KL) divergence as the proximal term. We make two contributions towards exploiting the geometry and structure of the variational bound. Firstly, we propose a KL proximal-point algorithm and show its equivalence to variational inference with natural gradients (e.g. stochastic variational inference). Secondly, we use the proximal framework to derive efficient variational algorithms for non-conjugate models. We propose a splitting procedure to separate non-conjugate terms from conjugate ones. We linearize the non-conjugate terms to obtain subproblems that admit a closed-form solution. Overall, our approach converts inference in a non-conjugate model to subproblems that involve inference in well-known conjugate models. We show that our method is applicable to a wide variety of models and can result in computationally efficient algorithms. Applications to real-world datasets show comparable performance to existing methods.

Presented at:
Advances in Neural Information Processing Systems (NIPS), Montreal, Canada, December 9, 2015

 Record created 2015-12-20, last modified 2019-08-12

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