Many particle-based Bayesian inference methods use a single global step size for all parts of the update. In Stein variational gradient descent (SVGD), however, each update combines two qualitatively different effects: attraction toward high-posterior regions and repulsion that preserves particle diversity. These effects can evolve at different rates, especially in high-dimensional, anisotropic, or hierarchical posteriors, so one step size can be unstable in some regions and inefficient in others. We derive a multirate version of SVGD that updates these components on different time scales. The framework yields practical algorithms, including a symmetric split method, a fixed multirate method (MR-SVGD), and an adaptive multirate method (Adapt-MR-SVGD) with local error control. We evaluate the methods in a broad and rigorous benchmark suite covering six problem families: a 50D Gaussian target, multiple 2D synthetic targets, UCI Bayesian logistic regression, multimodal Gaussian mixtures, Bayesian neural networks, and large-scale hierarchical logistic regression. Evaluation includes posterior-matching metrics, predictive performance, calibration quality, mixing, and explicit computational cost accounting. Across these six benchmark families, multirate SVGD variants improve robustness and quality-cost tradeoffs relative to vanilla SVGD. The strongest gains appear on stiff hierarchical, strongly anisotropic, and multimodal targets, where adaptive multirate SVGD is usually the strongest variant and fixed multirate SVGD provides a simpler robust alternative at lower cost.

翻译：许多基于粒子的贝叶斯推断方法在更新所有部分时使用单一的全局步长。然而，在斯坦变分梯度下降（SVGD）中，每次更新结合了两种性质不同的效应：向高后验区域吸引和保持粒子多样性的排斥力。这些效应可能以不同的速率演化，尤其是在高维、各向异性或层次化后验分布中，因此单一的步长可能在某些区域不稳定，而在其他区域效率低下。我们推导了一种多速率版本的SVGD，以不同的时间尺度更新这些组件。该框架产生了实用的算法，包括对称分裂法、固定多速率法（MR-SVGD）和具有局部误差控制的自适应多速率法（Adapt-MR-SVGD）。我们在一个广泛且严格的基准套件中评估了这些方法，涵盖六类问题：50维高斯目标、多个二维合成目标、UCI贝叶斯逻辑回归、多模态高斯混合模型、贝叶斯神经网络以及大规模层次化逻辑回归。评估指标包括后验匹配指标、预测性能、校准质量、混合特性以及显式计算成本核算。在这六个基准系列中，多速率SVGD变体相对于标准SVGD提高了鲁棒性和质量-成本权衡。最显著的改进出现在刚性层次化、强各向异性和多模态目标上，其中自适应多速率SVGD通常是最强的变体，而固定多速率SVGD以更低成本提供了更简单的鲁棒替代方案。