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.

本研究提出了一种新的变分推断方法，通过最小化切片Wasserstein距离来近似非规范化分布并使用神经网络对变分分布进行逼近。我们还提供了理论性分析，并用合成和实际数据进行了实验验证。

分片瓦烧斯坦变分推理