Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics

2026-07-22 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

The article introduces two new algorithms, LS-DuNeS and AU-DuNeS, for learning Gaussian Graphical Models (GGMs) from a single trajectory of random-scan Gaussian Glauber dynamics, addressing the challenge of dependent data where traditional independent sampling is unavailable. Existing techniques for this problem either inherit the chain's mixing time, which can be super-polynomial in dimension p, or are suboptimal in the minimum normalized edge strength κ, scaling as κ⁻⁵. The proposed algorithms are "mixing-free" and achieve the information-theoretic lower bound of κ⁻² dependence. Both instantiate a "dueling-neighborhood search meta-algorithm" (DuNeS). LS-DuNeS, using a least-squares regression statistic, requires O(pd²/κ²) updates and depends only logarithmically on the "degree-constrained spectral radius" ρ₂d(Θ). AU-DuNeS, based on an alternating-update pattern statistic, requires O(pd⁴/κ²) updates with no ρ₂d(Θ) dependence. The core innovation lies in extracting fresh Gaussian innovations from dependent, non-stationary observations. This research was published on July 19, 2026.

Key takeaway

For Machine Learning Engineers working with Gaussian Graphical Models where data originates from dependent stochastic processes like Glauber dynamics, you should consider adopting mixing-free algorithms such as LS-DuNeS or AU-DuNeS. These methods provide exact graph recovery with information-theoretically optimal κ⁻² dependence, avoiding the computational burden of mixing times or strong assumptions. This enables robust structure learning even in slow-mixing regimes, improving efficiency and reliability.

Key insights

Learning GGM structure from dependent Glauber dynamics is possible without mixing assumptions, achieving optimal κ⁻² dependence.

Principles

• Optimal κ⁻² dependence is achievable for GGM learning from Glauber dynamics.
• Mixing-free algorithms can outperform mixing-based methods in slow-mixing regimes.
• Fresh Gaussian innovations can be extracted from dependent, non-stationary observations.

Method

The DuNeS meta-algorithm employs a dueling-neighborhood search with local statistics built from update sequences. LS-DuNeS uses least-squares regression; AU-DuNeS uses alternating update patterns.

In practice

• Use LS-DuNeS for O(pd²/κ²) updates, tolerating slow mixing via logarithmic ρ₂d(Θ) dependence.
• Employ AU-DuNeS for O(pd⁴/κ²) updates when ρ₂d(Θ) is unknown or problematic.
• Apply DuNeS to structure learning problems with dependent, non-i.i.d. data.

Topics

• Gaussian Graphical Models
• Glauber Dynamics
• Structure Learning
• Mixing-Free Algorithms
• DuNeS Meta-Algorithm
• Sample Complexity

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

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