贝叶斯模型的推理是贝叶斯方法的核心研究。最常用的一类推理方法是变分推理，它具有收敛速度快和易并行化等优势，但是基于KL散度的传统变分推理会出现低估方差等问题，严重影响推理性能。因此学者们致力于研究使用更优的度量标准构建目标函数，从本质上提高变分推理的近似性能。目前，基于Wasserstein(W)距离的W变分推理表现出良好的推理性能和鲁棒性，相比于KL散度，W距离具有捕捉分布空间几何信息和对称性等许多优势。但现有W变分推理方法尚存在诸多问题严重影响应用效果：缺少通用的易于优化的目标函数和高精度的优化算法，推理效率低等。对此，本项目拟展开如下研究：使用copula函数和神经网络等构建通用的可近似计算的目标函数；降低蒙特卡洛估计方差提高计算精度；使用mini-batch和并行计算等策略提高推理速度。最终提出通用性良好、高精度、快速的W变分推理方法，为实际应用中的贝叶斯模型提供更准确高效的推理。

The central research of Bayesian learning is approximating inference of Bayesian models. Variational inference (VI) is one of the most widely used approximating inference methods, which tends to converge faster and be easier-to-parallelize. However, traditional variational inference based on Kullback-Leibler (KL) divergence suffers from problems such as underestimating variances, resulting in bad performance. Therefore, researchers have paid more attention to use better divergence measures to construct objective functions so as to gain more accurate variational approximations. Wasserstein VI has recently used Wasserstein distance as a divergence measure to construct the objective function, which has better performance and robustness. In contrast to KL divergence, Wasserstein distance can capture the geometry of distributions and has the appealing property of symmetry, leading to the superior performance. Unfortunately, the existing Wasserstein VI methods suffer from three issues: lack of general and approximate objective functions, lack of accurate approximations, and slow optimization. These results make the Wasserstein VI methods unavailable in real-world applications. To alleviate these issues, this project aims at improve Wasserstein VI methods by the following researches: using copulas and neural networks to construct general and approximate objectives; reducing variances of Monte Claro estimates to make more accurate approximations; speeding up inference through mini-batch and parallel computing. Finally, this project proposes a general, accurate and fast Wasserstein VI methodology, which can provide an effective and efficient inference for Bayesian models in applications.