标题： 半隐式变分推断通过核化路径梯度下降 显示英文标题

标题： Semi-Implicit Variational Inference via Kernelized Path Gradient Descent

摘要： 半隐式变分推断（SIVI）是一种用于近似复杂后验分布的强大框架，但由于高维设置下 Kullback-Leibler (KL) 散度的训练具有高方差和偏差，因此训练可能具有挑战性。虽然当前最先进的半隐式变分推断方法，特别是核半隐式变分推断（KSIVI），已被证明在高维情况下有效，但训练仍然相对昂贵。 在这项工作中，我们提出了一种核化的 KL 散度估计器，通过非参数平滑来稳定训练。为了进一步减少偏差，我们引入了重要性采样校正。我们提供了与 Stein 变分梯度下降的 amortized 版本的理论联系，该版本通过 Stein 恒等式估计分数梯度，表明两种方法最小化相同的目标，但我们的半隐式方法具有更低的梯度方差。此外，我们在函数空间中的方法偏差是良性的，从而导致更稳定和高效的优化。 实验结果表明，我们的方法在性能和训练效率方面优于或匹配最先进的 SIVI 方法。 显示英文摘要

摘要： Semi-implicit variational inference (SIVI) is a powerful framework for approximating complex posterior distributions, but training with the Kullback-Leibler (KL) divergence can be challenging due to high variance and bias in high-dimensional settings. While current state-of-the-art semi-implicit variational inference methods, particularly Kernel Semi-Implicit Variational Inference (KSIVI), have been shown to work in high dimensions, training remains moderately expensive. In this work, we propose a kernelized KL divergence estimator that stabilizes training through nonparametric smoothing. To further reduce the bias, we introduce an importance sampling correction. We provide a theoretical connection to the amortized version of the Stein variational gradient descent, which estimates the score gradient via Stein's identity, showing that both methods minimize the same objective, but our semi-implicit approach achieves lower gradient variance. In addition, our method's bias in function space is benign, leading to more stable and efficient optimization. Empirical results demonstrate that our method outperforms or matches state-of-the-art SIVI methods in both performance and training efficiency.