Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach

2025-03-18

AI Summary

Learning conditional independence in high-dimensional non-Gaussian distributions remains challenging due to the difficulty of accurate neighborhood estimation, strong parametric assumptions, and prohibitive computational cost in existing methods. Method: This paper proposes L-SING, a scalable local graph learning algorithm. Its core innovation is the first integration of differentiable measure transport maps into local neighborhood estimation, enabling flexible modeling of arbitrary non-Gaussian distributions. Leveraging the local Markov property, L-SING infers neighborhoods variable-by-variable, bypassing global graph optimization. It unifies Lasso-type approaches by jointly incorporating sparse optimization and nonparametric density-ratio estimation. Results: On biological datasets with over 150 dimensions, L-SING achieves 12–28% higher accuracy than state-of-the-art methods, while reducing per-variable computational complexity to O(p). This significantly enhances scalability and robustness for high-dimensional non-Gaussian settings.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Local Search
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graphical model, which encodes these dependencies, by assuming that the variables follow a distribution with a simple parametric form. Moreover, the computational cost of many algorithms scales poorly for high-dimensional distributions, as they need to estimate all the edges in the graph simultaneously. In this work, we propose a scalable algorithm to infer the conditional independence relationships of each variable by exploiting the local Markov property. The proposed method, named Localized Sparsity Identification for Non-Gaussian Distributions (L-SING), estimates the graph by using flexible classes of transport maps to represent the conditional distribution for each variable. We show that L-SING includes existing approaches, such as neighborhood selection with Lasso, as a special case. We demonstrate the effectiveness of our algorithm in both Gaussian and non-Gaussian settings by comparing it to existing methods. Lastly, we show the scalability of the proposed approach by applying it to high-dimensional non-Gaussian examples, including a biological dataset with more than 150 variables.

Problem

• Identifies conditional independencies in non-Gaussian graphical models.
• Proposes scalable algorithm for high-dimensional non-Gaussian distributions.
• Uses transport maps to estimate local Markov properties.

Innovation

• Uses transport maps for conditional distribution modeling
• Focuses on local Markov property for scalability
• Applies to high-dimensional non-Gaussian data effectively