Fast Variational Inference in the Conjugate Exponential Family
This work provides a general and faster optimization approach for probabilistic models in the conjugate exponential family, which is incremental as it builds on existing variational inference methods.
The authors tackled the problem of slow optimization in collapsed variational inference for conjugate exponential family models by deriving a new lower bound on the marginal likelihood and using information geometry to develop faster conjugate gradient methods, resulting in significant empirical speed-ups.
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. We exploit the information geometry of the bound to derive much faster optimization methods based on conjugate gradients for these models. Our approach is very general and is easily applied to any model where the mean field update equations have been derived. Empirically we show significant speed-ups for probabilistic models optimized using our bound.