论文标题
用群集融合正规化估计多个精度矩阵
Estimating Multiple Precision Matrices with Cluster Fusion Regularization
论文作者
论文摘要
我们提出了一个受惩罚的可能性框架，用于估计来自不同类别的多个精度矩阵。大多数现有的方法要么不包含有关精确矩阵之间关系的信息，要么需要此信息。本文提出的框架可以同时估算精度矩阵和精度矩阵之间的关系。提出了稀疏和非SPARSE估计器，这两者都需要解决非凸优化问题。为了计算我们提出的估计器，我们使用一种迭代算法，该算法在通过Blockwise坐标下降和K-均值聚类问题解决的凸优化问题之间交替。用于计算稀疏估计器的块更新需要解决弹性净惩罚精度矩阵估计问题，我们使用近端梯度下降算法解决该问题。我们证明该亚略词的收敛速率。在模拟研究和两个实际数据应用中，我们表明我们的方法可以胜过忽略精度矩阵之间相关关系的竞争者，并且与使用实际上经常在实践中经常知道的先前信息相似的方法。
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this information be known a priori. The framework proposed in this article allows for simultaneous estimation of the precision matrices and relationships between the precision matrices, jointly. Sparse and non-sparse estimators are proposed, both of which require solving a non-convex optimization problem. To compute our proposed estimators, we use an iterative algorithm which alternates between a convex optimization problem solved by blockwise coordinate descent and a k-means clustering problem. Blockwise updates for computing the sparse estimator require solving an elastic net penalized precision matrix estimation problem, which we solve using a proximal gradient descent algorithm. We prove that this subalgorithm has a linear rate of convergence. In simulation studies and two real data applications, we show that our method can outperform competitors that ignore relevant relationships between precision matrices and performs similarly to methods which use prior information often uknown in practice.
