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Structural causal models (SCMs) are widely used in various disciplines to represent causal relationships among variables in complex systems. Unfortunately, the true underlying directed acyclic graph (DAG) structure is often unknown, and determining it from observational or interventional data remains a challenging task. However, in many situations, the end goal is to identify changes (shifts) in causal mechanisms between related SCMs rather than recovering the entire underlying DAG structure. Examples include analyzing gene regulatory network structure changes between healthy and cancerous individuals or understanding variations in biological pathways under different cellular contexts. This paper focuses on identifying functional mechanism shifts in two or more related SCMs over the same set of variables -- without estimating the entire DAG structure of each SCM. Prior work under this setting assumed linear models with Gaussian noises; instead, in this work we assume that each SCM belongs to the more general class of nonlinear additive noise models (ANMs). A key contribution of this work is to show that the Jacobian of the score function for the mixture distribution allows for identification of shifts in general non-parametric functional mechanisms. Once the shifted variables are identified, we leverage recent work to estimate the structural differences, if any, for the shifted variables. Experiments on synthetic and real-world data are provided to showcase the applicability of this approach.
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Effective Causal Discovery under Identifiable Heteroscedastic Noise Model
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 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 heteroscedastic noise issue, we introduce relaxed implementable sufficient conditions and prove the identifiability of a general class of SEM subject to those conditions. Based on the identifiable general SEM, we propose a novel formulation for DAG learning which accounts for the noise variance variation across variables and observations. We then propose an effective two-phase iterative DAG learning algorithm to address the increasing optimization difficulties and learn a causal DAG from data with heteroscedastic variables 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.
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- Award ID(s):
- 2236026
- PAR ID:
- 10513288
- Publisher / Repository:
- AAAI
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 38
- Issue:
- 15
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 16486 to 16494
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1609/aaai.v38i15.29586
