具分解密度的字符串图（英文版）

英文标题：String Diagrams with Factorized Densities中文摘要：通过 Markov categories 定义无向图模型上的联合概率密度和样本结果的确定性映射的组合的范畴，这是将概率编程和因果推断中的因子化密度的操作定义与概率测度的范畴描述结合的一步。英文摘要：A growing body of research on probabilistic programs and causal models hashighlighted the need to reason compositionally about model classes that extenddirected graphical models. Both probabilistic programs and causal models definea joint probability density over a set of random variables, and exhibit sparsestructure that can be used to reason abou