Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data

2026-03-02 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

This paper introduces a Bayesian, moment-driven causal discovery framework designed to infer separate mean and variance causal graphs from observational heteroscedastic data. The framework addresses the limitations of standard causal discovery methods, which produce a single moment-agnostic graph, by explicitly distinguishing causes that influence a variable's conditional mean from those affecting its conditional variance. The authors derive identifiability conditions for these two distinct graphs, establishing sufficient conditions under which they can be separately identified. Building on this theory, a variational inference method is developed to learn a posterior distribution over both graphs, enabling principled uncertainty quantification of structural features like edges and paths. To optimize parameters in complex heteroscedastic models with dual graph structures, the method employs a curvature-aware optimization approach and incorporates prior domain knowledge on node orderings to enhance sample efficiency. Experiments on synthetic, semi-synthetic, and real-world data, including the Sachs dataset, demonstrate that this approach accurately recovers mean and variance structures, outperforming existing baselines and showing robustness to non-Gaussian noise.

Key takeaway

For AI Researchers and Causal Inference Scientists working with complex, heteroscedastic observational data, adopting this moment-driven causal discovery framework can significantly improve the interpretability of causal mechanisms. Your intervention strategies can become more targeted by distinguishing between mean- and variance-level causes, as demonstrated in drug design and systems biology. Consider integrating prior knowledge about node orderings to boost sample efficiency, especially in data-scarce scenarios, and leverage the Bayesian approach for robust uncertainty quantification.

Key insights

Separating mean and variance causal influences improves interpretability and intervention design in heteroscedastic systems.

Principles

• Heteroscedasticity requires moment-specific causal graphs.
• Gaussian noise is crucial for moment-based cause separation.
• Prior knowledge improves sample efficiency in causal discovery.

Method

A Bayesian variational inference framework learns posterior distributions over separate mean and variance causal graphs, using differentiable DAG sampling and curvature-aware optimization for heteroscedastic models.

In practice

• Use for drug discovery to refine compound effects.
• Apply in systems biology to detect variance modulators.
• Enhance algorithmic fairness by identifying latent sensitive attributes.

Topics

• Causal Discovery
• Heteroscedasticity
• Mean-Variance Causal Graphs
• Variational Inference
• Bayesian Causal Discovery

Code references

• rjbgoudie/structmcmc
• naiyuyin/ICDH
• baosws/HOST
• PayamDiba/SERGIO

Best for: AI Researcher, AI Scientist, Research Scientist

Related on AIssential

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• Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability — Persistent homology enables identifying causal effects on outcome distribution shapes, addressing limitations of mean-based estimands.
• Unsupervised Causal Abstractions Discovery — This work proposes an unsupervised method to discover high-level causal abstractions directly from low-level observational data.
• Tensor-based second-order causal discovery — TSCD uses second-order statistics from observational and interventional data to efficiently discover causal graphs and functions, scaling to hundreds of variables.
• Instrumental and Proximal Causal Inference with Gaussian Processes — DGP provides reliable epistemic uncertainty quantification for IV and Proxy causal inference, recovering kernel estimators.

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.