Identifying homogeneous subgroups of variables can be challenging in high dimensional data analysis with highly correlated predictors. We propose a new method called Hexagonal Operator for Regression with Shrinkage and Equality Selection, HORSES for short, that simultaneously selects positively correlated variables and identifies them as predictive clusters. This is achieved via a constrained least-squares problem with regularization that consists of a linear combination of an L_1 penalty for the coefficients and another L_1 penalty for pairwise differences of the coefficients. This specification of the penalty function encourages grouping of positively correlated predictors combined with a sparsity solution. We construct an efficient algorithm to implement the HORSES procedure. We show via simulation that the proposed method outperforms other variable selection methods in terms of prediction error and parsimony. The technique is demonstrated on two data sets, a small data set from analysis of soil in Appalachia, and a high dimensional data set from a near infrared (NIR) spectroscopy study, showing the flexibility of the methodology.
Contraction of a quasi-Bayesian model with shrinkage priors in precision matrix estimation
目前有几种贝叶斯方法可用于估计大型稀疏精度矩阵，包括贝叶斯图形Lasso（Wang，2012），贝叶斯结构学习（Banerjee和Ghosal，2015）和图形马蹄铁（Li et al.，2019年）。虽然这些方法表现出很好的经验性能，但一般来说，它们的计算成本很高。此外，我们对理论性质的了解有限，例如，后验收缩率，图形贝叶斯套索和图形马蹄铁。在本文中，我们提出了一种新的方法，集成了一些常用的连续收缩先验到一个准贝叶斯框架的特点是伪似然。在适当的条件下，我们建立了一个最佳的后验收缩率所提出的方法。与现有的方法相比，我们的方法有两个主要优点。首先，我们的方法在计算上更有效，同时实现类似的错误率;其次，我们的框架更适合理论分析。大量的模拟实验和实际数据集上的分析支持我们的理论结果。
Bayesian DAG Structure Learning with Simultaneous Shrinkage Covariance Estimation under Scale-Mixture Error Distributions in the Proportional High-Dimensional Regime
Ferdowsi University of Mashhad（马什哈德 Ferdowsi 大学）；North Carolina Agricultural and Technical State University（北卡罗来纳农业与技术州立大学）
Horseshoe Regularization for Machine Learning in Complex and Deep Models
自从正则化的马蹄先验出现以来，全局-局部收缩方法已被证明是机器学习中贝叶斯方法发展的沃土，特别是对于高维回归和分类问题。它们在计算上取得了显著的成功，并得到了强有力的理论支持。大多数现有文献都集中在线性高斯情况下;参见Bhadra et al.（2019 b）进行系统调查。本文的目的是通过回顾与机器学习应用更相关的复杂模型中的方法和计算发展，证明马蹄正则化的有用性。具体来说，我们专注于非线性和非高斯模型中的马蹄正则化方法的挑战;多变量模型;和深度神经网络。我们还概述了最近的计算马蹄形收缩的复杂模型的发展，以及可用的软件实现列表，允许一个冒险超出舒适区的典型线性回归问题。
Learning Compositional Sparse Gaussian Processes with a Shrinkage Prior
Ulsan National Institute of Science and Technology（蔚山国立科学技术院）；VinAI Research（VinAI研究院）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；INEEJI
