Effective Causal Discovery under Identifiable Heteroscedastic Noise Model
This addresses a key limitation in causal discovery for AI applications where real-world data often has varying noise, but it is an incremental improvement over existing optimization frameworks.
The paper tackles the problem of causal discovery under heteroscedastic noise, which violates common assumptions in existing methods, by introducing identifiable conditions and a novel DAG learning formulation, resulting in significant empirical gains over state-of-the-art methods on synthetic and real data.
Capturing the underlying structural causal relations represented by Directed Acyclic Graphs (DAGs) has been a fundamental task in various AI disciplines. Causal DAG learning via the continuous optimization framework has recently achieved promising performance in terms of both accuracy and efficiency. However, most methods make strong assumptions of homoscedastic noise, i.e., exogenous noises have equal variances across variables, observations, or even both. The noises in real data usually violate both assumptions due to the biases introduced by different data collection processes. To address the issue of heteroscedastic noise, we introduce relaxed and implementable sufficient conditions, proving the identifiability of a general class of SEM subject to these conditions. Based on the identifiable general SEM, we propose a novel formulation for DAG learning that accounts for the variation in noise variance across variables and observations. We then propose an effective two-phase iterative DAG learning algorithm to address the increasing optimization difficulties and to learn a causal DAG from data with heteroscedastic variable noise under varying variance. We show significant empirical gains of the proposed approaches over state-of-the-art methods on both synthetic data and real data.