Two-Stage Variance Approximation for Heteroscedastic Causal Discovery

TMLR Paper9309 Authors

Abstract: Learning causal structures from observational data is difficult when noise variances are unequal or depend on parent values (heteroscedasticity). We propose a two‑stage framework that decouples structure learning from variance estimation. Instead of modeling full variance functions, we use a variance‑matrix approximation: node‑wise constant variances expanded across samples, refined by a small, bounded per‑sample correction. We show that, under heteroscedastic causal models, the optimal constant surrogate equals the expected conditional variance, and the residual approximation error is a scale‑invariant gap. We develop practical centralized and federated algorithms using stabilizers, including variance clipping and a progressive variance floor. Extensive empirical studies on both synthetic and real-world data show that our proposed approach discovers more plausible causal structures than competing baselines.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Lu_Zhang3

Submission Number: 9309