fDAG-ACDC: Uncertainty-Adaptive Factor-Count Selection for High-Dimensional Causal Discovery

Causal representation learning (CRL) methods aim to discover low-dimensional representations whose components correspond to the mechanisms that generate high-dimensional observations. Changing the number of latent components affects the interpretation of the inferred mechanisms, yet the correct number of mechanisms is rarely known. Hence there is a need for model-selection criteria to determine the number of components. However, existing criteria are generally inapplicable to CRL models because adding latent structure can improve global fit by absorbing misspecification rather than capturing distinct mechanisms. In this work, we address this gap, focusing on factor-directed acyclic graphs (f-DAGs) as a test case. We introduce fDAG-ACDC, an uncertainty-adaptive extension of the accumulated cutoff discrepancy criterion (ACDC), which compares observed and posterior-predictive distributions of each node and its estimated parents within each perturbation environment. Theoretically, we prove model selection consistency of fDAG-ACDC under intuitive conditions. In simulations, fDAG-ACDC's mean absolute selection error is just 0.5, while validation likelihood and oracle graph-recovery baselines over-select by more than 3 on average. On Perturb-seq and organoid data, fDAG-ACDC selects fewer factors than validation likelihood while matching or nearly matching larger models in predicting biological summaries, and its Perturb-seq factors are enriched for known gene programs.