The most fundamental problem in statistical causality is determining causal
relationships from limited data. Probability trees, which combine prior causal
structures with Bayesian updates, have been suggested as a possible solution.
In this work, we quantify the information gain from a single intervention and
show that both the anticipated information gain, prior to making an
intervention, and the expected gain from an intervention have simple
expressions. This results in an active-learning method that simply selects the
intervention with the highest anticipated gain, which we illustrate through
several examples. Our work demonstrates how probability trees, and Bayesian
estimation of their parameters, offer a simple yet viable approach to fast
causal induction.

本文主要研究如何从有限的数据中确定因果关系 —— 通过将先前的因果结构与贝叶斯估计相结合，该文提出了概率树作为可能的解决方案。研究发现，单一干预的信息增益、干预前的预期信息增益以及干预后预期得到的信息增益都有简单的表达式。因此给出了一种主动学习方法，即选择预期增益最高的干预方式，并通过几个例子予以说明；同时，该方法也展示了概率树及其参数的贝叶斯估计提供了一种简单而可行的快速因果归纳方法。

概率树与单一干预价值

Probability trees and the value of a single intervention

Probability trees are one of the simplest models of causal generative
processes. They possess clean semantics and -- unlike causal Bayesian networks
-- they can represent context-specific causal dependencies, which are necessary
for e.g. causal induction. Yet, they have received little attention from the AI
and ML community. Here we present concrete algorithms for causal reasoning in
discrete probability trees that cover the entire causal hierarchy (association,
intervention, and counterfactuals), and operate on arbitrary propositional and
causal events. Our work expands the domain of causal reasoning to a very
general class of discrete stochastic processes.

文章介绍了离散概率树的因果推理算法，能够覆盖整个因果层次（相关性、干预和反事实），并能应用于任意命题和因果事件，扩展了因果推理的范畴。

概率树中因果推理的算法

Algorithms for Causal Reasoning in Probability Trees

This papers develops a logical language for representing probabilistic causal
laws. Our interest in such a language is twofold. First, it can be motivated as
a fundamental study of the representation of causal knowledge. Causality has an
inherent dynamic aspect, which has been studied at the semantical level by
Shafer in his framework of probability trees. In such a dynamic context, where
the evolution of a domain over time is considered, the idea of a causal law as
something which guides this evolution is quite natural. In our formalization, a
set of probabilistic causal laws can be used to represent a class of
probability trees in a concise, flexible and modular way. In this way, our work
extends Shafer's by offering a convenient logical representation for his
semantical objects.
Second, this language also has relevance for the area of probabilistic logic
programming. In particular, we prove that the formal semantics of a theory in
our language can be equivalently defined as a probability distribution over the
well-founded models of certain logic programs, rendering it formally quite
similar to existing languages such as ICL or PRISM. Because we can motivate and
explain our language in a completely self-contained way as a representation of
probabilistic causal laws, this provides a new way of explaining the intuitions
behind such probabilistic logic programs: we can say precisely which knowledge
such a program expresses, in terms that are equally understandable by a
non-logician. Moreover, we also obtain an additional piece of knowledge
representation methodology for probabilistic logic programs, by showing how
they can express probabilistic causal laws.

本文介绍了一种逻辑语言，用于表示概率因果律，该语言可以被用于概率逻辑编程，并且可以自我解释为概率因果律的表示方法，从而提供了解释这些编程背后想法的新方法。