This article proposes a Bayesian approach to regression with a continuous scalar response and an undirected network predictor. Undirected network predictors are often expressed in terms of symmetric adjacency matrices, with rows and columns of the matrix representing the nodes, and zero entries signifying no association between two corresponding nodes. Network predictor matrices are typically vectorized prior to any analysis, thus failing to account for the important structural information in the network. This results in poor inferential and predictive performance in presence of small sample sizes. We propose a novel class of network shrinkage priors for the coefficient corresponding to the undirected network predictor. The proposed framework is devised to detect both nodes and edges in the network predictive of the response. Our framework is implemented using an efficient Markov Chain Monte Carlo algorithm. Empirical results in simulation studies illustrate strikingly superior inferential and predictive gains of the proposed framework in comparison with the ordinary high dimensional Bayesian shrinkage priors and penalized optimization schemes. We apply our method to a brain connectome dataset that contains information on brain networks along with a measure of creativity for multiple individuals. Here, interest lies in building a regression model of the creativity measure on the network predictor to identify important regions and connections in the brain strongly associated with creativity. To the best of our knowledge, our approach is the first principled Bayesian method that is able to detect scientifically interpretable regions and connections in the brain actively impacting the continuous response (creativity) in the presence of a small sample size.

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具有无向网络预测器的贝叶斯回归以及对大脑连接组数据的应用

本文提出了一种具有连续标量响应和无向网络预测器的贝叶斯回归方法。无向网络预测器通常用对称邻接矩阵表示，矩阵的行和列代表节点，零项表示两个对应节点之间没有关联。网络预测矩阵通常在任何分析之前进行矢量化，因此无法考虑网络中的重要结构信息。这会导致在样本量较小的情况下推理和预测性能较差。我们为对应于无向网络预测器的系数提出了一类新的网络收缩先验。所提出的框架旨在检测网络中预测响应的节点和边。我们的框架是使用高效的马尔可夫链蒙特卡罗算法实现的。模拟研究中的实证结果表明，与普通的高维贝叶斯收缩先验和惩罚优化方案相比，所提出的框架具有显着优越的推理和预测收益。我们将我们的方法应用于大脑连接组数据集，该数据集包含有关大脑网络的信息以及对多个人的创造力的衡量。在这里，兴趣在于在网络预测器上建立创造力度量的回归模型，以识别大脑中与创造力密切相关的重要区域和连接。据我们所知，