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Intervention and Conditioning in Causal Bayesian Networks

NeurIPS 2024 · Probabilistic and scientific modeling › Causal discovery · approach: Causal effect identification · 0 citations (OpenAlex)

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Gives a formal semantics for interventional formulas in Causal Bayesian Networks under an independence assumption on CPT entries, making probabilities of necessity and sufficiency identifiable from observational data in many settings.

Problem

Probabilities of formulas combining interventions and conditioning are not well defined in CBNs; Pearl's procedure gives incorrect results and yields only ranges of values rather than unique probabilities.

Approach

Assume the mechanisms (CPT entries for different parent settings and different variables) are mutually independent, which lets interventional formulas get a unique probability via complete combinations of conditional events; shows any CBN has an i-compatible causal model built with response-function exogenous variables, and that PN and PS become identifiable from observational conditional probabil

Key results

• Under the independence assumption, the probability of an interventional formula in a CBN is uniquely determined, as a sum of products of CPT entries.
• Worked example: Pr_M*(X=0 and Y=0 and [X<-1](Y=1)) = 1/4 under independence versus 1/2 in a compatible model without independence.
• Probabilities of necessity and sufficiency can be computed from conditional probabilities of simple (intervention-free) formulas, estimable from observational data.

Surprising findings

• Pearl's stated abduction-action-prediction procedure for CBNs gives an incorrect answer; a trivial counterexample yields p(X=1|X=1)=1/2 instead of 1.

Limitations

• Independence of conditional events for different parent settings is a strong assumption that may not hold when latent exogenous variables affect Y across parent settings.
• Results are theoretical with no empirical evaluation on data.
• Full details of some proofs are deferred or left to the reader.

Experimental setup

Baselines: Pearl's three-step procedure for CBNs Tian and Pearl bounds on probability of necessity and sufficiency

Builds on: Pearl's causal models Balke and Pearl bounds Richardson and Halpern independence result d-separation

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