Title: Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach Show Chinese title

Title: 非高斯图模型的局部邻域学习：基于度量传输的方法

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. Show Chinese abstract

Abstract: 识别一组随机变量的马尔可夫性质或条件独立性是统计学中建模和推理的一项基本任务。现有方法通常通过假设变量遵循具有简单参数形式的分布来学习概率图模型的结构，从而编码这些依赖关系。此外，许多算法的计算成本对于高维分布来说扩展性较差，因为它们需要同时估计图中的所有边。在这项工作中，我们提出了一种可扩展的算法，通过利用局部马尔可夫性质来推断每个变量的条件独立关系。该方法名为“非高斯分布的局部稀疏性识别”（L-SING），使用灵活的传输映射类来表示每个变量的条件分布以估计图。我们表明，L-SING 包含现有的方法，如带有 Lasso 的邻域选择，作为特例。我们通过将其与现有方法进行比较，证明了该算法在高斯和非高斯情况下的有效性。最后，我们通过将其应用于包含超过 150 个变量的生物数据集等高维非高斯例子，展示了所提出方法的可扩展性。