Wasserstein Gradient Flow over Variational Parameter Space for Variational Inference
This work addresses the efficiency of optimization in variational inference for machine learning practitioners, but it appears incremental as it reinterprets existing methods within a new framework.
The paper tackles the optimization problem in variational inference by reframing it as optimizing probability distributions over variational parameter space and proposing Wasserstein gradient descent, showing that existing methods like black-box VI and natural-gradient VI are specific instances of this approach, with empirical validation on a synthetic dataset.
Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached through vanilla gradient descent in black-box VI or natural-gradient descent in natural-gradient VI. In this work, we reframe VI as the optimization of an objective that concerns probability distributions defined over a \textit{variational parameter space}. Subsequently, we propose Wasserstein gradient descent for tackling this optimization problem. Notably, the optimization techniques, namely black-box VI and natural-gradient VI, can be reinterpreted as specific instances of the proposed Wasserstein gradient descent. To enhance the efficiency of optimization, we develop practical methods for numerically solving the discrete gradient flows. We validate the effectiveness of the proposed methods through empirical experiments on a synthetic dataset, supplemented by theoretical analyses.