A Forest Mixture Bound for Block-Free Parallel Inference
This addresses the computational bottleneck in probabilistic inference for researchers and practitioners, though it is incremental as it builds on existing variational methods.
The paper tackles the slow speed of coordinate ascent variational inference by developing a stable parallel algorithm for deep exponential families that avoids variable partitioning, showing empirically faster convergence for forest-like models with Gaussian variables.
Coordinate ascent variational inference is an important algorithm for inference in probabilistic models, but it is slow because it updates only a single variable at a time. Block coordinate methods perform inference faster by updating blocks of variables in parallel. However, the speed and stability of these algorithms depends on how the variables are partitioned into blocks. In this paper, we give a stable parallel algorithm for inference in deep exponential families that doesn't require the variables to be partitioned into blocks. We achieve this by lower bounding the ELBO by a new objective we call the forest mixture bound (FM bound) that separates the inference problem for variables within a hidden layer. We apply this to the simple case when all random variables are Gaussian and show empirically that the algorithm converges faster for models that are inherently more forest-like.