论文标题
正规化的Stein变分梯度流动
Regularized Stein Variational Gradient Flow
论文作者
论文摘要
Stein变异梯度下降（SVGD）算法是采样的确定性粒子方法。然而，平均场分析表明，与SVGD算法相对应的梯度流（即，Stein变异梯度流）仅提供与瓦斯恒星梯度流相对应与Kl-Divergence最小化相对应的恒定阶近似。在这项工作中，我们提出了正规化的Stein变异梯度流，该梯度流在Stein变化梯度流和Wasserstein梯度流之间进行了插值。我们建立了正则化的Stein变分梯度流（及其时间限制）的各种理论特性，包括融合弱溶液的平衡，存在和唯一性以及溶液的稳定性。我们提供了正规化提供的改善性能的初步数值证据。
The Stein Variational Gradient Descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient Flow) only provides a constant-order approximation to the Wasserstein Gradient Flow corresponding to the KL-divergence minimization. In this work, we propose the Regularized Stein Variational Gradient Flow, which interpolates between the Stein Variational Gradient Flow and the Wasserstein Gradient Flow. We establish various theoretical properties of the Regularized Stein Variational Gradient Flow (and its time-discretization) including convergence to equilibrium, existence and uniqueness of weak solutions, and stability of the solutions. We provide preliminary numerical evidence of the improved performance offered by the regularization.
