Kantorovich Continuity of Probabilistic Programs.
arXiv: Logic in Computer Science(2019)
摘要
The Kantorovich metric is a canonical lifting of a distance from sets to distributions over this set. The metric also arises naturally when proving continuity properties of probabilistic programs. For instance, algorithmic stability of machine learning algorithms is upper bounded by the maximal Kantorovich distance between program executions, for a suitable notion of metric on the underlying space. Motivated by these applications, we develop a sound method to approximate the Kantorovich distance between two executions of a probabilistic program. Our method takes the form of a relational pre-expectation calculus. We illustrate our methods for proving stability of machine learning algorithms and convergence of probabilistic processes.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络