An Information Theoretic Measure of Judea Pearl's Identifiability and Causal Influence
This work addresses the fundamental challenge of causal inference in AI and statistics by providing rigorous tools for identifiability, which is crucial for researchers and practitioners in fields like machine learning, epidemiology, and social sciences, though it is incremental as it builds on existing do-calculus and algorithms.
The paper tackles the problem of determining when causal effects are identifiable in graphical models by introducing a new information-theoretic measure called 'uprooted information', which provides a necessary and sufficient condition for identifiability, and presents an algorithm for deciding identifiability in semi-Markovian Bayesian nets, correcting a flaw in prior work. It also establishes a necessary and sufficient graphical condition for identifiability when the intervention set is a singleton, improving upon previous sufficient-only conditions.
In this paper, we define a new information theoretic measure that we call the "uprooted information". We show that a necessary and sufficient condition for a probability $P(s|do(t))$ to be "identifiable" (in the sense of Pearl) in a graph $G$ is that its uprooted information be non-negative for all models of the graph $G$. In this paper, we also give a new algorithm for deciding, for a Bayesian net that is semi-Markovian, whether a probability $P(s|do(t))$ is identifiable, and, if it is identifiable, for expressing it without allusions to confounding variables. Our algorithm is closely based on a previous algorithm by Tian and Pearl, but seems to correct a small flaw in theirs. In this paper, we also find a {\it necessary and sufficient graphical condition} for a probability $P(s|do(t))$ to be identifiable when $t$ is a singleton set. So far, in the prior literature, it appears that only a {\it sufficient graphical condition} has been given for this. By "graphical" we mean that it is directly based on Judea Pearl's 3 rules of do-calculus.