[Paper] Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventions

Source: arXiv - 2603.02204v1

Overview

Selective conformal prediction promises tighter, data‑driven uncertainty estimates—but only when the calibration points truly resemble the test point. In many scientific and engineering settings (e.g., gene‑perturbation experiments), this “exchangeability” holds only within subsets of interventions that leave the target variable untouched. The paper tackles the realistic scenario where the underlying causal invariance structure is unknown and must be inferred from the data itself, delivering a robust way to keep conformal coverage guarantees even when the learned structure is imperfect.

Key Contributions

• Contamination‑robust coverage theorem – Derives a finite‑sample lower bound on conformal coverage that explicitly accounts for the fraction δ of mis‑identified calibration points, via a function (g(δ,n)). The bound holds for any contaminating distribution.
• Partial causal learning formulation – Instead of reconstructing the full causal graph, the authors propose learning only the binary descendant indicators (Z_{a,i} = \mathbf{1}{i \in \text{desc}(a)}) needed for selective calibration.
• Algorithms for descendant discovery –
  1. Perturbation‑intersection method: exploits overlapping sets of variables affected by different interventions to infer descendant relationships.
  2. Local invariant causal prediction (ICP) estimator: provides an approximate “distance‑to‑intervention” score for each variable.
• Theoretical recovery conditions – Guarantees that, under mild assumptions on the intervention design, the learned descendant set mis‑classification rate stays below a controllable δ.
• Empirical validation – Synthetic linear SEM experiments confirm that the corrected selective conformal procedure maintains ≥ 95 % coverage even with 30 % contamination, while the naïve method drops to ≈ 86 %. A proof‑of‑concept on real CRISPRi perturbation data (Replogle K562) shows the approach works on high‑dimensional genomics screens.

Methodology

1. Problem framing – In an interventional dataset, each experiment (a) intervenes on a subset of variables. For a target variable (Y), only calibration points from interventions that do not affect (Y) (i.e., (Y) is not a descendant of the intervened node) are exchangeable with a test point drawn under the same intervention.
2. Partial causal learning – Rather than learning the full DAG, the method learns a binary matrix (Z) where each entry tells whether variable (i) is a descendant of intervention (a). This is sufficient to decide which calibration examples to keep.
3. Descendant discovery via intersection patterns –
   • For each intervention, record the set of variables whose distribution changes (detected by simple two‑sample tests).
   • Intersections of these “affected” sets across multiple interventions reveal common descendants, allowing a rule‑based construction of (Z).
4. Local ICP for distance‑to‑intervention – Treat each variable as a potential “target” and run invariant causal prediction on subsets of interventions. The resulting p‑value profile yields a soft score indicating how far the variable lies from the intervention source.
5. Contamination‑aware conformal inference – Apply standard split‑conformal prediction on the selected calibration set, then adjust the prediction interval using the bound (g(δ,n)) to guarantee the desired coverage despite possible mis‑classifications.

All steps are computationally lightweight (linear‑time set operations, standard hypothesis tests, and off‑the‑shelf ICP implementations), making the pipeline feasible for large‑scale perturbation studies.

Results & Findings

Key take‑aways

• The coverage bound is tight: even when up to 30 % of calibration points are wrongly included, the corrected intervals still meet the nominal guarantee.
• The learned descendant matrix (Z) is accurate enough in practice to enable selective calibration, yielding substantially narrower prediction sets compared with using the whole calibration pool.

Practical Implications

• Genomics & drug discovery – Researchers can run high‑throughput perturbation screens (CRISPR, RNAi, chemical knock‑downs) and obtain reliable confidence intervals for downstream predictions (e.g., gene‑expression response, phenotype likelihood) without sacrificing statistical guarantees.
• A/B testing & online experimentation – In platforms where interventions (feature flags, UI changes) affect only a subset of downstream metrics, the method can isolate the “unaffected” calibration data, leading to tighter uncertainty bounds for key performance indicators.
• Robust ML pipelines – The contamination‑aware conformal correction can be dropped into any existing conformal prediction library (e.g., mapie, conformal‑inference) as a preprocessing filter, making it easy for developers to adopt.
• Resource efficiency – By learning only the binary descendant indicators, the approach avoids the combinatorial explosion of full causal discovery, enabling deployment on datasets with thousands of variables and hundreds of interventions.

Limitations & Future Work

• Assumption of identifiable affected sets – The intersection‑based method relies on being able to detect distributional changes per intervention; noisy measurements or weak effects may lead to higher δ.
• Linear SEM focus in experiments – Synthetic validation uses linear structural equation models; extending guarantees to nonlinear or non‑Gaussian settings remains an open question.
• Scalability of local ICP – While feasible for moderate dimensions, ICP can become costly for tens of thousands of variables; future work could explore approximate or neural‑based invariance tests.
• Dynamic interventions – The current framework assumes a static set of interventions; handling time‑varying or adaptive interventions (e.g., reinforcement‑learning policies) would broaden applicability.

Overall, the paper bridges causal inference and conformal prediction, offering a pragmatic tool for developers who need trustworthy uncertainty quantification in intervention‑rich environments.

Authors

• Amir Asiaee
• Kavey Aryan
• James P. Long

Paper Information

• arXiv ID: 2603.02204v1
• Categories: cs.LG, stat.ML
• Published: March 2, 2026
• PDF: Download PDF