Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventions

TL;DR

This paper develops a robust conformal inference method for causal settings with interventions, learning only the necessary causal structure to improve uncertainty quantification in complex, real-world data.

Contribution

It introduces a contamination-robust coverage theorem, a task-driven causal learning approach for descendant identification, and algorithms for intervention analysis, advancing selective conformal inference under unknown invariance.

Findings

Validated the coverage bound on synthetic SEMs with up to 30% contamination

Maintained ≥ 0.95 coverage under contamination, outperforming uncorrected methods

Demonstrated applicability on real genomic CRISPR perturbation data

Abstract

Selective conformal prediction can yield substantially tighter uncertainty sets when we can identify calibration examples that are exchangeable with the test example. In interventional settings, such as perturbation experiments in genomics, exchangeability often holds only within subsets of interventions that leave a target variable "unaffected" (e.g., non-descendants of an intervened node in a causal graph). We study the practical regime where this invariance structure is unknown and must be learned from data. Our contributions are: (i) a contamination-robust conformal coverage theorem that quantifies how misclassification of "unaffected" calibration examples degrades coverage via an explicit function $g(\delta,n)$ of the contamination fraction and calibration set size, providing a finite-sample lower bound that holds for arbitrary contaminating distributions; (ii) a task-driven partial causal learning formulation that estimates only the binary descendant indicators $Z_{a,i}=\mathbf{1}\{i\in\mathrm{desc}(a)\}$ needed for selective calibration, rather than the full causal graph; and (iii) algorithms for descendant discovery via perturbation intersection patterns (differentially affected variable set intersections across interventions), and for approximate distance-to-intervention estimation via local invariant causal prediction. We provide recovery conditions under which contamination is controlled. Experiments on synthetic linear structural equation models (SEMs) validate the bound: under controlled contamination up to $\delta=0.30$, the corrected procedure maintains $\ge 0.95$ coverage while uncorrected selective CP degrades to $0.867$. A proof-of-concept on Replogle K562 CRISPR interference (CRISPRi) perturbation data demonstrates applicability to real genomic screens.