Statistical Inference for Causal Discovery under Selection and Latent Variables via Single-Target Interventions

This paper develops a model-free framework for causal discovery when observed data are distorted by latent confounding and selection bias, using soft single-target interventions. Its central construct, the system-induced subgraph, isolates causal relations among system variables while treating context variables as nuisance factors. The authors represent these relations with maximal ancestral graphs and prove that intervening on every observed system variable, K=d_X, is both sufficient and worst-case necessary for uniquely identifying the trimmed combined-MAG. A two-stage procedure first estimates intervention-induced anterior sets with conditional two-sample tests, then performs parallel conditional-independence and invariance tests for adjacency and orientation, providing asymptotic family-wise error control. It requires at most 2.5d_X^2 statistical tests, while any constraint-based method needs at least 0.5d_X(d_X−1), establishing optimality up to a constant. Simulations use d_X=20 variables and 500 samples per regime, including negative-binomial Perturb-seq-like data; misspecified methods such as F-FCI or procedures that ignore selection show substantially inflated false-discovery rates. In a Perturb-seq analysis of interferon-β-stimulated A549 lung cancer cells, the method reduced the system to 51 target genes from 27,555 cells, inferred 246 graph edges, identified 6 selection ancestors, and flagged 200 gene pairs with evidence of latent confounding. The framework supports downstream tests for selection and confounding without parametric structural-equation assumptions.