An Asymptotically Optimal Coordinate Descent Algorithm for Learning Bayesian Networks from Gaussian Models

2024-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new coordinate descent algorithm has been developed for learning Bayesian networks from continuous observational data, specifically those generated by a linear Gaussian structural equation model. This algorithm approximates an $\ell_0$-penalized maximum likelihood estimator, which is statistically robust but computationally intensive for medium-sized networks. The proposed method is proven to converge to a coordinate-wise minimum. Notably, as sample size increases, its objective value converges to the optimal objective value of the $\ell_0$-penalized estimator, a first for coordinate descent procedures in this context. Numerical experiments using both synthetic and real-world datasets confirm that the algorithm achieves near-optimal solutions while maintaining scalability.

Key takeaway

For research scientists working with Bayesian network learning from continuous Gaussian data, this algorithm offers a computationally scalable approach with strong theoretical guarantees. You should consider integrating this coordinate descent method, especially when dealing with $\ell_0$-penalized maximum likelihood estimators, as it provides near-optimal solutions without the typical computational burden.

Key insights

A new coordinate descent algorithm offers provable optimality guarantees for learning Bayesian networks from Gaussian data.

Principles

• $\ell_0$-penalized MLE offers favorable statistical properties.
• Coordinate descent can approximate non-convex estimators.
• Asymptotic optimality is achievable for non-convex problems.

Method

The method uses a coordinate descent algorithm to approximate an $\ell_0$-penalized maximum likelihood estimator for linear Gaussian structural equation models, converging to a coordinate-wise minimum.

In practice

• Apply to continuous observational data.
• Use for medium-sized Bayesian networks.
• Leverage provided code for implementation.

Topics

• Bayesian Networks
• Coordinate Descent
• $\ell_0$-Penalization
• Gaussian Models
• Asymptotic Optimality

Code references

• AtomXT/coordinate-descent-for-bayesian-networks

Best for: Research Scientist, AI Researcher, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.