AI 中文总结
该研究将吉布斯采样和CAVI的收敛速率分析从均匀块选择扩展到任意固定正选择概率，提出适配选择的凸性常数，为异构块几何的扫描适配提供了原则性方法。
AI 中文摘要
吉布斯采样（Gibbs sampling）和坐标上升变分推断（coordinate ascent variational inference, CAVI）是统计计算中两种基础的逐坐标方法。近期在强对数凹性假设下的分析，为每一步更新一个均匀选择的块的这些算法版本建立了收敛速率。我们将这两个结果扩展到任意固定的严格正选择概率。这些速率由一个适配选择的凸性常数λ*_θ决定，该常数利用块平滑度常数和选择概率θ定义。同一常数会使吉布斯采样的相对熵收缩，也会使随机扫描CAVI的平均场目标间隙收缩。新的界恢复了均匀扫描的结果，且绝不弱于基于最小选择概率的朴素比较，它们提供了一种利用曲率信息使扫描适配异构块几何的原则性方法。
英文摘要
Gibbs sampling and coordinate ascent variational inference (CAVI) are two basic coordinate-wise methods for statistical computation. Recent analyses under strong log-concavity establish convergence rates for versions of these algorithms that update one uniformly selected block at each step. We extend both results to arbitrary fixed, strictly positive selection probabilities. The rates are governed by a selection-adapted convexity constant $λ^{\star}_θ$, defined using the block-smoothness constants and the selection probabilities $θ$. The same constant yields a contraction of relative entropy for the Gibbs sampler and a contraction of the mean-field objective gap for random-scan CAVI. The new bounds recover the uniform-scan results, and are never weaker than the naive comparison based on the smallest selection probability. They provide a principled way to adapt the scan to heterogeneous block geometry using curvature information.
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