跨越因果層次的概率推理（CS LO）

• 2020 年 1 月 14 日
• 筆記

我們建議將關聯、介入和反事實的三層因果層次正式化，作為一系列概率邏輯語言。我們的語言具有嚴格的表達能力，第一種語言能夠表達定量的概率推理——包括條件獨立和貝葉斯推理——第二種語言能夠編碼因果關係的演算推理，第三種語言能夠表達任意反事實查詢的演算推理。給出了結構因果模型和概率程式上相應的完備的有限公理，並證明了在多項式空間上，每種語言的可滿足性和有效性是可判定的。

原文題目：Probabilistic Reasoning across the Causal Hierarchy

原文：We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning—including conditional independence and Bayesian inference—the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable in polynomial space.

原文作者：Duligur Ibeling, Thomas Icard

原文地址：https://arxiv.org/abs/2001.02889