Estimation of High-Dimensional Graphical Models Using Regularized Score Matching.
Estimation of High-Dimensional Graphical Models Using Regularized Score Matching.
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DOI：
10.1214/16-ejs1126
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发表时间：
2016
影响因子：
1.1
通讯作者：
Shojaie A
中科院分区：
文献类型：
--
作者：
Lin L;Drton M;Shojaie A
图形模型被广泛用于模拟大量变量之间的随机依赖关系。我们介绍了一种基于分数匹配损失估计无向条件独立图的新方法，由。我们提出的正则化分数匹配方法适用于具有连续观测的设置，并允许对可能的非高斯指数族模型进行有效的计算处理。在经过充分探索的高斯设置下，正则化分数匹配避免了应用邻域选择技术时出现的不对称问题，并且与直接产生对称估计的现有方法相比，分数匹配方法的优点是所考虑的损失是二次的，并且在1正则化下给出分段线性解路径。在适当的不可表示性条件下，我们证明了在稀疏高维设置下，1-正则化分数匹配对于图估计是一致的。通过数值实验和对RNAseq数据的应用，我们证实了正则化分数匹配在高斯情况下达到了最先进的性能，并为非高斯图形模型的计算效率估计提供了一个有价值的工具。
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, and subsequently extended in. 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 ℓ1 regularization. Under suitable irrepresentability conditions, we show that ℓ1-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.