arXiv:2503.13899cs.LGstat.CO2025-03AAAI被引 1

提出新方法L-SING,高效推断非高斯图模型的局部依赖关系。

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

论文配图:Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach
图 1 · 摘自论文原文
  • 用可变传输映射建模每个变量的条件分布,实现局部独立性推断
  • 在150+变量的生物数据上验证了算法有效性和可扩展性
  • 适用于非高斯场景,比传统方法更灵活,计算成本更低

识别随机变量间的马尔可夫性质或条件独立性是统计建模与推断中的基础任务。现有方法通常假设变量服从简单参数分布,并需同时估计图中所有边,导致高维情形下计算成本过高。本文提出一种可扩展算法——局部稀疏性识别非高斯分布(L-SING),通过利用每个变量的局部马尔可夫性质,采用灵活的传输映射类来表示条件分布,从而估计图结构。我们证明,该方法包含带Lasso的邻域选择等已有方法作为特例。在高斯与非高斯设置下,实验对比表明其有效性;进一步在超过150个变量的生物数据上展示了良好可扩展性。

原文摘要 · Abstract (English)

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.

图模型非高斯可扩展条件独立

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