Structured regularization for conditional Gaussian graphical models
Structured regularization for conditional Gaussian graphical models
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DOI：
10.1007/s11222-016-9654-1
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发表时间：
2017-05-01
影响因子：
2.2
通讯作者：
Robin, Stephane
中科院分区：
文献类型：
--
作者：
Chiquet, Julien;Mary-Huard, Tristan;Robin, Stephane
条件高斯图模型是多元线性回归模型的重新参数化，它显式显示（i）预测变量和响应之间的偏协方差，以及（ii）响应本身之间的偏协方差。这种模型特别适合解释，因为偏协方差描述变量之间的直接关系。在这个框架中，我们提出了一个正则化方案，以提高模型的学习策略，通过先验结构信息驱动相关输入特征的选择。它带有一个有效的交替优化过程，保证收敛到全局最小值。除了在人工和真实的数据集上表现出有竞争力的性能外，我们的方法还展示了精细解释的能力，如光谱学，遗传学和基因组学的三个高维数据集所示。
Conditional Gaussian graphical models are a reparametrization of the multivariate linear regression model which explicitly exhibits (i) the partial covariances between the predictors and the responses, and (ii) the partial covariances between the responses themselves. Such models are particularly suitable for interpretability since partial covariances describe direct relationships between variables. In this framework, we propose a regularization scheme to enhance the learning strategy of the model by driving the selection of the relevant input features by prior structural information. It comes with an efficient alternating optimization procedure which is guaranteed to converge to the global minimum. On top of showing competitive performance on artificial and real datasets, our method demonstrates capabilities for fine interpretation, as illustrated on three high-dimensional datasets from spectroscopy, genetics, and genomics.