论文标题
基于广义的贝叶斯贝叶斯方法，用于可扩展的关节回归和协方差选择。
A generalized likelihood based Bayesian approach for scalable joint regression and covariance selection in high dimensions
论文作者
论文摘要
本文解决了回归系数矩阵中的关节稀疏性选择以及贝叶斯范式中高维多元回归模型的误差精度（逆协方差）矩阵。所选的稀疏模式对于帮助了解预测变量和响应变量之间的关系网络以及后者之间的条件关系至关重要。尽管贝叶斯方法的优势是通过后置换概率和可靠的间隔提供自然的不确定性定量，但当前的贝叶斯方法要么限于稀疏模式的特定子类，而且/或不可扩展到具有数百个响应和预测因子的设置。仅关注后验模式的贝叶斯方法是可扩展的，但不会从后验分布中产生样品以进行不确定性定量。 Using a bi-convex regression based generalized likelihood and spike-and-slab priors, we develop an algorithm called Joint Regression Network Selector (JRNS) for joint regression and covariance selection which (a) can accommodate general sparsity patterns, (b) provides posterior samples for uncertainty quantification, and (c) is scalable and orders of magnitude faster than the state-of-the-art Bayesian approaches providing不确定性定量。我们通过分析选定的癌症数据集证明了所提出的方法对拟议方法的统计和计算功效。我们还为一种发达算法建立了高维后一致性。
The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity patterns are crucial to help understand the network of relationships between the predictor and response variables, as well as the conditional relationships among the latter. While Bayesian methods have the advantage of providing natural uncertainty quantification through posterior inclusion probabilities and credible intervals, current Bayesian approaches either restrict to specific sub-classes of sparsity patterns and/or are not scalable to settings with hundreds of responses and predictors. Bayesian approaches which only focus on estimating the posterior mode are scalable, but do not generate samples from the posterior distribution for uncertainty quantification. Using a bi-convex regression based generalized likelihood and spike-and-slab priors, we develop an algorithm called Joint Regression Network Selector (JRNS) for joint regression and covariance selection which (a) can accommodate general sparsity patterns, (b) provides posterior samples for uncertainty quantification, and (c) is scalable and orders of magnitude faster than the state-of-the-art Bayesian approaches providing uncertainty quantification. We demonstrate the statistical and computational efficacy of the proposed approach on synthetic data and through the analysis of selected cancer data sets. We also establish high-dimensional posterior consistency for one of the developed algorithms.
