This study focuses on learning causal directed acyclic graphs (DAGs) under heteroscedastic noise models (HNMs), where each effect is modeled as a function of its causes and a Gaussian noise term whose variance depends on the causes. While HNMs theoretically guarantee identifiability of causal structures, we show that gradient-based continuous DAG learning can fail in practice due to an adverse interaction between heteroscedastic likelihood optimization and the acyclicity constraint. Specifically, because the reconstruction gradient is scaled by the predicted variance, it can be heavily attenuated in early training; as a result, the DAG parameters may be updated primarily by the acyclicity constraint before the data reconstruction signal is sufficiently learned, hindering effective structure learning. We identify and formalize this failure mode. To mitigate it, we propose a graduated optimization strategy based on a surrogate loss that decouples the variance term from the reconstruction loss, thereby preventing early gradient attenuation. We further introduce a scheduling coefficient that initially assigns a high weight to the surrogate loss for stable mean learning, and then gradually transitions to the full heteroscedastic likelihood to refine variance estimates and strictly enforce acyclicity. This strategy avoids the identified failure mode and guides the learned DAG to better reflect the data. Experimental results on both synthetic and real-world datasets verify the effectiveness of our approach. Our Github repository including code and supplementary material is here: https://github.com/Sinegi/HNM.
Eunjung Choi, Seonggyeom Kim, Dong-Kyu Chae· Proceedings of the 32nd ACM...· 0 citations
Causal Structure-guided DRO (CS-DRO) is proposed, which estimates a directed acyclic graph (DAG) that encodes the predictive relationships between representations and labels, serving as a proxy for causal structure shared across source domains.
Seonggyeom Kim, Eunjung Choi, Dong-Kyu Chae· Proceedings of the 32nd ACM...· 0 citations
Domain generalization (DG) aims to learn predictive models from multiple source domains that maintain performance on unseen target domains. Distributionally robust optimization (DRO) addresses distribution shift by minimizing the worst-case risk over an uncertainty set of plausible test distributions. However, if this uncertainty set is overly large, it may include unrealistic shifts, leading to low-confidence predictions. To address this issue, we propose Causal Structure-guided DRO (CS-DRO), which estimates a directed acyclic graph (DAG) that encodes the predictive relationships between representations and labels, serving as a proxy for causal structure shared across source domains. Using gradient-based signals, we quantify how well the candidate distributions explored during optimization maintain the estimated structure and impose a structure-preserving constraint on the uncertainty set. The resulting DRO objective is reformulated via Lagrangian relaxation into a tractable primal–dual learning problem. Experiments on standard DG benchmarks show that our method achieves competitive performance compared to state-of-the-art methods while improving robustness to unseen target domains. Our Github repository including code and supplementary material is here: https://github.com/gyeomo/CS-DRO.
Seonggyeom Kim, Eunjung Choi, Dong-Kyu Chae· Proceedings of the 32nd ACM...· 0 citations
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