Intervention and Conditioning in Causal Bayesian Networks
This work addresses a key problem for researchers and practitioners in causal inference by providing a method to estimate intervention probabilities without experiments, though it is incremental as it builds on existing CBN frameworks.
The paper tackles the challenge of estimating probabilities for interventional formulas in Causal Bayesian Networks by introducing simple independence assumptions, enabling unique estimation from observational data in many practical cases.
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.