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Optimal Experiments for Partial Causal Effect Identification

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Identifiability with hidden confounders · 0 citations (OpenAlex)

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Formalizes selecting cost-constrained experiments to maximally tighten partial-identification bounds on causal queries (max-potency), proves NP-hardness, and prunes candidates via graphical criteria (path-interception and ID check).

Problem

Given a causal graph, observational distribution, and budget, which ex-ante subset of experiments most tightens worst-case bounds on a partially identifiable causal query; the search space is super-exponential in variables and potency evaluation requires polynomial programs.

Approach

Defines epistemic potency as the guaranteed worst-case reduction in bound width from an experiment set, proves NP-hardness via 0-1 knapsack, and certifies zero-potency experiments from the causal graph alone (district-based path interception and the ID algorithm), making ID-pruned experiments inert in subset search.

Key results

• On Erdős–Rényi graphs, pruning removes on average 74.3% ± 19.4% of 200 candidate experiments (33.0% via ID check, 41.3% via interception).
• On 11 bnlearn networks, the two criteria prune on average 63.4% ± 12.4% of candidates.
• On NHANES, the optimal single experiment at B=1 is P(y_{x'}, y'_x) with potency 0.48; at B=3 the pair {P(y_{x'},y'_x), P(Y|do(x'))} gives potency 0.85.

Surprising findings

• The optimal experiment choice changes with the width criterion: under best-case width, a different candidate is selected at B=1 than under worst-case width.
• Under the worst-case criterion, an experiment that appears informative singly (P(X,Y|do(z))) ranks low, while a counterfactual experiment dominates.

Limitations

• Requires a known ADMG, discrete variables with finite support, and exact observational distribution.
• Pruning criteria are sound but not complete; some non-pruned experiments may still have zero potency.
• Worst-case width criterion may select different sets than alternative criteria.

Experimental setup

Datasets: Erdős–Rényi random ADMGs bnlearn benchmark networks NHANES 2017-2018

Benchmarks: Erdős–Rényi random graphs bnlearn networks NHANES physical activity–diabetes case study

Metrics: fraction of candidate experiments pruned epistemic potency bound width

Builds on: polynomial programming bounds (Zhang et al.) ID algorithm c-factor decomposition response-type variables

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