A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1

通过虚拟粒子随机逼近实现的可证明快速的有限粒子SVGD变体

Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximation

针对有限粒子SVGD行为研究不足的问题，提出VP-SVGD和GB-SVGD两种高效变体，通过虚拟粒子随机逼近实现快速收敛，给出了多项式维数依赖的预言复杂度，收敛性较现有分析有双指数提升。

SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence

Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of optimal transport. We introduce a new perspective on SVGD that instead views SVGD as the (kernelized) gradient flow of the chi-squared divergence which, we show, exhibits a strong form of uniform exponential ergodicity under conditions as weak as a Poincaré inequality. This perspective leads us to propose an alternative to SVGD, called Laplacian Adjusted Wasserstein Gradient Descent (LAWGD), that can be implemented fr…

朗之万正则化SVGD的定量目标收敛性与时不变混沌传播

Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD

该研究针对朗之万正则化SVGD，建立了其定量目标收敛性与时不变混沌传播的理论结果，推导了相关界并对比了两种有限时间机制的性能。

粒子梯度下降的误差界限，以及对 log-Sobolev 和 Talagrand 不等式的扩展

Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities

本文证明了粒子梯度下降（PGD）的非渐近误差界限，通过扩展 log-Sobolev 和 Polyak--Łojasiewicz 不等式及 Bakry--Émery 定理，证明了在强凹对数似然模型下该流指数收敛并控制了离散化误差。

Kernel-based L_2-Boosting with Structure Constraints

Developing efficient kernel methods for regression is very popular in the past decade. In this paper, utilizing boosting on kernel-based weaker learners, we propose a novel kernel-based learning algorithm called kernel-based re-scaled boosting with truncation, dubbed as KReBooT. The proposed KReBooT benefits in controlling the structure of estimators and producing sparse estimate, and is near overfitting resistant. We conduct both theoretical analysis and numerical simulations to illustrate the power of KReBooT. Theoretically, we prove that KReBooT can achieve the almost optimal numerical conv…

受约束的 Stein 变分轨迹优化

Constrained Stein Variational Trajectory Optimization

本文提出 CSVTO 算法，将受约束轨迹优化构建为对轨迹分布的受约束泛函最小化，利用 SVGD 生成满足约束的多样化轨迹集合，有效避免局部极小值，在高度约束任务中优于基线方法。