Verifying formulas for interventional distributions

Francesco Freni; Leonard Henckel; Sebastian Weichwald

stat.MEJul 15, 2026

Verifying formulas for interventional distributions

Authors: Francesco Freni, Leonard Henckel, Sebastian Weichwald

Organizations: Department of Mathematical Sciences, University of Copenhagen, Denmark · School of Mathematics and Statistics, University College Dublin, Ireland

Abstract

We formalize verification in causal graphical models: deciding whether a given observational formula identifies a target interventional distribution. This opens a problem complementary to identification, asking not whether any identifying formula exists, but whether the given formula is identifying. We show that even sound and complete solutions to identification do not solve verification. We propose a falsifier as a first practical route forward, prove that it induces an almost-surely correct verifier for regular exponential-family models, and use the resulting verifier to develop the gateway test, which finds all sets admissible for use in a front-door formula.

Explore similar work

Adversarial Causal Intervention Falsification
Aug 5, 2026Mojtaba EslamiCausal Reasoning
Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs
Jun 2, 2026Clément Yvernes, Emilie Devijver, Marianne Clausel +1Causal Graph Causal Reasoning
CIVeX: Causal Intervention Verification for Language Agents
May 9, 2026Fabio RovaiCausal Intervention Causal Reasoning

Aug 5, 2026 · cs.LGJ/K move · Enter open · S save

Adversarial Causal Intervention Falsification

Mojtaba Eslami

University of Calgary

Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.

Causal Reasoning

Open paper Ask about it PDF

Abstract

Explore similar work

Adversarial Causal Intervention Falsification

Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs

CIVeX: Causal Intervention Verification for Language Agents