Sliced Wasserstein Variational Inference
This addresses the problem of improving variational inference for machine learning practitioners by offering a more robust alternative to KL divergence, though it appears incremental as it builds on existing optimal transport concepts.
The authors tackled the limitations of Kullback-Leibler divergence in variational inference by proposing a new method that minimizes sliced Wasserstein distance, a valid metric from optimal transport, which allows for approximation without optimization and supports amortized generators like neural networks, with experiments demonstrating its performance on synthetic and real data.
Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some unreasonable properties. For example, it is not a proper metric, i.e., it is non-symmetric and does not preserve the triangle inequality. On the other hand, optimal transport distances recently have shown some advantages over KL divergence. With the help of these advantages, we propose a new variational inference method by minimizing sliced Wasserstein distance, a valid metric arising from optimal transport. This sliced Wasserstein distance can be approximated simply by running MCMC but without solving any optimization problem. Our approximation also does not require a tractable density function of variational distributions so that approximating families can be amortized by generators like neural networks. Furthermore, we provide an analysis of the theoretical properties of our method. Experiments on synthetic and real data are illustrated to show the performance of the proposed method.