Probability trees and the value of a single intervention

TL;DR

This paper introduces a method using probability trees and Bayesian updates to quantify the information gained from a single intervention, enabling efficient causal discovery through active learning.

Contribution

It provides simple expressions for expected information gain from interventions and demonstrates an active-learning approach for causal inference using probability trees.

Findings

Expected information gain expressions are derived for interventions.

Active learning method effectively identifies the most informative interventions.

Probability trees facilitate fast causal induction with Bayesian parameter estimation.

Abstract

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.