Original title: Causal Discovery under Identifiable Heteroscedastic Noise Model
Authors: Naiyu Yin, Tian Gao, Yue Yu, Qiang Ji
The article discusses the importance of capturing the structural causal relationships represented by Directed Acyclic Graphs (DAGs) in various AI disciplines. It highlights how recent advancements in causal DAG learning through continuous optimization have shown promising results in terms of accuracy and efficiency. However, most existing methods assume homoscedastic noise, meaning that exogenous noises have equal variances across variables and observations. This assumption is unrealistic for real data, which often violates both conditions due to biases introduced during data collection.
To tackle the issue of heteroscedastic noise, the article introduces relaxed and implementable sufficient conditions that prove the identifiability of a general class of SEM (Structural Equation Model) subject to these conditions. Building upon this identified general SEM, the article proposes a novel formulation for DAG learning that takes into account the variation in noise variance across variables and observations. To address the challenge of increasing optimization difficulties, an effective two-phase iterative DAG learning algorithm is proposed. The proposed approaches are shown to have significant empirical gains over state-of-the-art methods when tested on both synthetic and real data.
Original article: https://arxiv.org/abs/2312.12844