标题： 高维图形模型的正则化得分匹配估计 显示英文标题

标题： Estimation of High-Dimensional Graphical Models Using Regularized Score Matching

摘要： 图模型被广泛用于建模大量变量之间的随机依赖关系。我们引入了一种基于 Hyvärinen（2005）提出的得分匹配损失的新方法，用于估计无向条件独立图，并在 Hyvärinen（2007）中进一步扩展。我们提出的正则化得分匹配方法适用于连续观测的场景，并允许对可能非高斯的指数族模型进行计算高效的处理。在广为人知的高斯设定下，正则化得分匹配避免了邻域选择技术中出现的不对称问题，与现有直接产生对称估计的方法相比，得分匹配方法的优势在于所考虑的损失函数是二次的，并且在 $\ell_1$ 正则化下可以给出分段线性解路径。在适当的不可表征性条件下，我们证明了 $\ell_1$-正则化得分匹配在稀疏高维设定下的图估计是一致的。通过数值实验和对 RNAseq 数据的应用，我们确认正则化得分匹配在高斯情况下实现了最先进的性能，并为非高斯图模型的计算高效估计提供了一个有价值的工具。 显示英文摘要

摘要： Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by Hyvarinen (2005), and subsequently extended in Hyvarinen (2007). The regularized score matching method we propose applies to settings with continuous observations and allows for computationally efficient treatment of possibly non-Gaussian exponential family models. In the well-explored Gaussian setting, regularized score matching avoids issues of asymmetry that arise when applying the technique of neighborhood selection, and compared to existing methods that directly yield symmetric estimates, the score matching approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under $\ell_1$ regularization. Under suitable irrepresentability conditions, we show that $\ell_1$-regularized score matching is consistent for graph estimation in sparse high-dimensional settings. Through numerical experiments and an application to RNAseq data, we confirm that regularized score matching achieves state-of-the-art performance in the Gaussian case and provides a valuable tool for computationally efficient estimation in non-Gaussian graphical models.