Regularized matrix regression.
Regularized matrix regression.
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DOI：
10.1111/rssb.12031
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发表时间：
2014-03-01
期刊：
影响因子：
--
通讯作者：
Li L
中科院分区：
文献类型：
--
作者：
Zhou H;Li L
现代技术正在产生大量具有复杂结构的数据。例如，在二维数字成像、流式细胞术和脑电图中，当针对两个基础变量的每个组合获得测量值时，经常出现矩阵型协变量。为了解决这些数据产生的科学问题，需要采用矩阵作为协变量的新回归方法，由于矩阵数据的多维性和复杂结构，稀疏性或其他形式的正则化至关重要。流行的套索和相关的正则化方法取决于真实信号的稀疏性（根据其非零系数的数量）。然而，对于矩阵数据，真实信号通常是低秩结构，或者可以很好地近似于低秩结构。因此，稀疏性通常是以矩阵参数的低秩的形式，这可能严重违反经典套索的假设。提出了一类基于谱正则化的正则化矩阵回归方法。提出了一种高效、可扩展的估计算法，推导了沿正则化路径沿着选择模型的自由度公式，并通过仿真和真实的算例验证了该方法的上级性能.
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry and electroencephalography, matrix-type covariates frequently arise when measurements are obtained for each combination of two underlying variables. To address scientific questions arising from those data, new regression methods that take matrices as covariates are needed, and sparsity or other forms of regularization are crucial owing to the ultrahigh dimensionality and complex structure of the matrix data. The popular lasso and related regularization methods hinge on the sparsity of the true signal in terms of the number of its non-zero coefficients. However, for the matrix data, the true signal is often of, or can be well approximated by, a low rank structure. As such, the sparsity is frequently in the form of low rank of the matrix parameters, which may seriously violate the assumption of the classical lasso. We propose a class of regularized matrix regression methods based on spectral regularization. A highly efficient and scalable estimation algorithm is developed, and a degrees-of-freedom formula is derived to facilitate model selection along the regularization path. Superior performance of the method proposed is demonstrated on both synthetic and real examples.
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