论文标题
平均场变异推断通过瓦斯恒星梯度流动
Mean-field Variational Inference via Wasserstein Gradient Flow
论文作者
论文摘要
变异推断（例如平均场（MF）近似）需要某些共轭结构才能有效计算。这些可以对可行的先前分布家族施加不必要的限制，并对变异近似家族施加进一步的限制。在这项工作中，我们介绍了一个通用的计算框架，以使用Wasserstein梯度流（WGF）（一种现代的数学技术来实现概率测量空间的梯度流量），以实现有或没有潜在变量的贝叶斯模型的MF变异推断。从理论上讲，我们分析了所提出方法的算法收敛，为收缩因子提供了明确的表达。我们还通过利用时间限制的WGF的固定点方程来加强MF变异后浓度的现有结果。在计算上，我们使用神经网络提出了一种新的无约束函数近似方法，以数值实现我们的算法。与基于langevin动力学的传统粒子近似方法相比，该方法比传统的粒子近似方法更精确和高效。
Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on the variational approximation family. In this work, we introduce a general computational framework to implement MF variational inference for Bayesian models, with or without latent variables, using the Wasserstein gradient flow (WGF), a modern mathematical technique for realizing a gradient flow over the space of probability measures. Theoretically, we analyze the algorithmic convergence of the proposed approaches, providing an explicit expression for the contraction factor. We also strengthen existing results on MF variational posterior concentration from a polynomial to an exponential contraction, by utilizing the fixed point equation of the time-discretized WGF. Computationally, we propose a new constraint-free function approximation method using neural networks to numerically realize our algorithm. This method is shown to be more precise and efficient than traditional particle approximation methods based on Langevin dynamics.
