提出坐标上升变分推断的Wasserstein收缩理论，适用于多种复杂模型。
Wasserstein Contraction of Coordinate Ascent Variational Inference
- 基于优化映射光滑性与运输信息不等式，分析三类坐标上升算法收敛性
- 首次在非凸、离散及高维模型中建立严格收敛结果，包含伊辛模型等
- 适合研究变分推断理论或处理复杂贝叶斯模型的科研人员
本文研究了序列、并行和随机扫描三种坐标上升变分推断算法在Wasserstein距离下的非渐近收缩性质。该性质在最优映射的函数光滑性条件以及其不动点处的运输-信息不等式下成立。结果具有普适性和紧致性，不同于依赖全局强对数凹假设的已有结论，可实现对光滑、非光滑及离散流形上的局部收敛，包括数据增强场景。应用于统计物理与贝叶斯统计中的多种模型，如成对马尔可夫随机场（如伊辛模型和居里-韦斯模型）、非平衡贝叶斯高斯混合模型、高维贝叶斯概率回归及使用波兰-盖拉随机变量的高维逻辑回归（即Jaakkola-Jordan算法）。在其中许多模型中，这是首份相关收敛性结果。
原文摘要 · Abstract (English)
We study the non-asymptotic contraction in Wasserstein distance of the sequential, parallel, and random-scan coordinate ascent variational inference algorithms. This is shown to hold under a functional smoothness condition of the optimality maps and a transportation-information inequality at their fixed points. Our results are sharp and general, and as opposed to those based on global strong log-concavity assumptions, they allow for local convergence on smooth, non-smooth, and discrete manifolds, including within the context of data augmentation. We consider many applications in statistical physics and Bayesian statistics. These include pairwise Markov Random field models such as Ising and Curie-Weiss, unbalanced Bayesian Gaussian Mixture Models, high-dimensional Bayesian Probit Regression, and high-dimensional Logistic Regression with Pólya--Gamma random variables (i.e. Jaakkola-Jordan's algorithm). In many of these models, these represent the first available convergence results of their kind.
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