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

Abstract

Causal discovery from observational and interventional data becomes challenging in the presence of latent confounding and selection bias, where causal structure is no longer adequately represented by directed acyclic graphs over observed variables. Existing model-free methods often rely on an exponential number of conditional independence tests and provide limited uncertainty quantification in high-dimensional settings. We develop a model-free and constraint-query optimal statistical inference framework for causal discovery under latent variables and selection using single-target interventions. We introduce the system-induced subgraph (SIS) to capture the causal relations among system variables while accounting for context variables. We establish its identifiability through maximal ancestral graphs (MAGs), and show that interventions on each observed system variable are sufficient for unique identification and necessary in the worst case. Building on these results, we develop a two-stage graph inference procedure with asymptotic family-wise error control under sufficient first-stage power. For $d_X$ observed system variables, the procedure requires at most $\frac{5}{2}d_X^2$ statistical tests, parallelizable within each stage, and achieves optimal constraint-query complexity up to a constant factor. The framework accommodates soft interventions and avoids parametric structural equation assumptions. We illustrate the methods through analysis of Perturb-seq data from interferon-$\beta$-stimulated A549 lung cancer cell lines.