用斯泰因方法实现更精准的概率推断与学习
Probabilistic Inference and Learning with Stein's Method
- 基于斯泰因算子和斯泰因集构造可计算的差异度量
- 实现收敛检测与控制，提升推断稳定性
- 适合概率建模与贝叶斯推断研究者参考
本专著系统梳理了概率推断与学习中斯泰因方法的理论与方法。提供了从斯泰因算子和斯泰因集构建斯泰因差异度量的具体方法，并讨论了这些度量的可计算性、分离性、收敛检测与收敛控制等性质。详细阐明了斯泰因算子与斯泰因变分梯度下降之间的联系。所有核心定义与结果均严格表述，且提供完整证明引用。
原文摘要 · Abstract (English)
This monograph provides a rigorous overview of theoretical and methodological aspects of probabilistic inference and learning with Stein's method. Recipes are provided for constructing Stein discrepancies from Stein operators and Stein sets, and properties of these discrepancies such as computability, separation, convergence detection, and convergence control are discussed. Further, the connection between Stein operators and Stein variational gradient descent is set out in detail. The main definitions and results are precisely stated, and references to all proofs are provided.
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