Intervention and Conditioning in Causal Bayesian Networks

TL;DR

This paper explores how simple independence assumptions in Causal Bayesian Networks enable the unique estimation of interventional probabilities from observational data, facilitating causal inference without extensive experimentation.

Contribution

It introduces realistic independence assumptions that allow for the estimation of interventional probabilities in CBNs using observational data, expanding causal analysis capabilities.

Findings

Unique estimation of interventional probabilities under certain assumptions

Applicability of assumptions in practical causal inference scenarios

Potential to evaluate causal probabilities without experimental data

Abstract

Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose significant challenges. In case of Causal Bayesian Networks (CBNs), Pearl assumes autonomy of mechanisms that determine interventions to calculate a range of probabilities. We show that by making simple yet often realistic independence assumptions, it is possible to uniquely estimate the probability of an interventional formula (including the well-studied notions of probability of sufficiency and necessity). We discuss when these assumptions are appropriate. Importantly, in many cases of interest, when the assumptions are appropriate, these probability estimates can be evaluated using observational data, which carries immense significance in scenarios where conducting experiments is impractical or unfeasible.