论文标题
纵向数据的大型非组织协方差矩阵的融合式 - 正规化cholesky因子
Fused-Lasso Regularized Cholesky Factors of Large Nonstationary Covariance Matrices of Longitudinal Data
论文作者
论文摘要
大协方差矩阵的cholesky因子的分子的平滑度与时间序列和纵向数据的自回归模型的非组织性程度密切相关。启发式上，人们期望近乎固定的协方差矩阵倾斜因子的每个子基因的条目几乎是相同的，因为连续项的绝对值之和很小。从统计上讲，这种平滑度是通过使用融合型拉索惩罚来正规化每个细胞对角线来实现这种平滑度。我们依靠标准的Cholesky因子作为正常的正常似然设置中的新参数，该参数可以保证：（1）可能性函数的联合凸性，（2）即使在$ n <p $，（3）估计的估计的COVARIXS MATRIX的正质量时，可能会严格限制了可能限制在每个子数字的可能性函数。提出了一个块坐标下降算法，其中每个块是一个亚对角线，并在轻度条件下建立了其收敛性。缺乏将惩罚的似然函数脱钩到涉及单个子差异的功能之和的总和，这会引起一些计算挑战和优势，相对于两种最近的算法，用于稀疏估计Cholesky因子的稀疏估计，这些算法是将行以排除行的稀疏估计。仿真结果和实际数据分析显示了所提出的方法的范围和良好性能。
Smoothness of the subdiagonals of the Cholesky factor of large covariance matrices is closely related to the degrees of nonstationarity of autoregressive models for time series and longitudinal data. Heuristically, one expects for a nearly stationary covariance matrix the entries in each subdiagonal of the Cholesky factor of its inverse to be nearly the same in the sense that sum of absolute values of successive terms is small. Statistically such smoothness is achieved by regularizing each subdiagonal using fused-type lasso penalties. We rely on the standard Cholesky factor as the new parameters within a regularized normal likelihood setup which guarantees: (1) joint convexity of the likelihood function, (2) strict convexity of the likelihood function restricted to each subdiagonal even when $n<p$, and (3) positive-definiteness of the estimated covariance matrix. A block coordinate descent algorithm, where each block is a subdiagonal, is proposed and its convergence is established under mild conditions. Lack of decoupling of the penalized likelihood function into a sum of functions involving individual subdiagonals gives rise to some computational challenges and advantages relative to two recent algorithms for sparse estimation of the Cholesky factor which decouple row-wise. Simulation results and real data analysis show the scope and good performance of the proposed methodology.
