标题： 高维线性回归中的贝叶斯最优学习与网络侧信息 显示英文标题

标题： Bayes optimal learning in high-dimensional linear regression with network side information

摘要： 带有时空信息的监督学习问题在基因组学、蛋白质组学和神经科学的应用中经常出现。 例如，在遗传应用中，网络时空信息可以准确捕捉有关相关基因之间复杂关系的背景生物学信息。 在本文中，我们开始研究具有网络时空信息的高维线性回归中的贝叶斯最优学习。 为此，我们首先引入一个简单的生成模型（称为 Reg-Graph 模型），该模型通过一组共同的潜在参数为监督数据和观察到的网络提供联合分布。 接下来，我们引入一种基于近似消息传递（AMP）的迭代算法，在非常一般的条件下，该算法被证明是贝叶斯最优的。 此外，我们表征了潜在信号和观察到的数据之间的极限互信息，从而精确量化了网络时空信息的统计影响。 最后，支持性的数值实验表明，所引入的算法在有限样本中表现出色。 显示英文摘要

摘要： Supervised learning problems with side information in the form of a network arise frequently in applications in genomics, proteomics and neuroscience. For example, in genetic applications, the network side information can accurately capture background biological information on the intricate relations among the relevant genes. In this paper, we initiate a study of Bayes optimal learning in high-dimensional linear regression with network side information. To this end, we first introduce a simple generative model (called the Reg-Graph model) which posits a joint distribution for the supervised data and the observed network through a common set of latent parameters. Next, we introduce an iterative algorithm based on Approximate Message Passing (AMP) which is provably Bayes optimal under very general conditions. In addition, we characterize the limiting mutual information between the latent signal and the data observed, and thus precisely quantify the statistical impact of the network side information. Finally, supporting numerical experiments suggest that the introduced algorithm has excellent performance in finite samples.