Bayesian Low Rank and Sparse Covariance Matrix Decomposition
Bayesian Low Rank and Sparse Covariance Matrix Decomposition
复制标题
贝叶斯低秩稀疏协方差矩阵分解
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
B. Mallick
中科院分区：
文献类型：
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作者：
Lin Zhang;A. Sarkar;B. Mallick
我们考虑的问题，估计高维协方差矩阵的一个特定的结构，这是一个低秩和稀疏矩阵的总和。这种协方差结构具有广泛的应用，包括因子分析和随机效应模型。我们提出了一个贝叶斯方法估计的协方差矩阵表示的协方差模型的形式与未知数量的潜在因素的因素模型。我们引入二元指标的因素选择和秩估计的低秩分量结合贝叶斯套索方法的稀疏分量估计。仿真结果表明，该方法可以恢复的秩以及稀疏的两个组件分别。我们进一步将我们的方法扩展到图形因子模型，其中残差的图形模型以及选择因子的数量是感兴趣的。我们采用超逆Wishart先验建模的残差可分解的图形，和贝叶斯图形套索选择方法的不受限制的图形。我们通过模拟表明，扩展模型可以恢复的潜在因素的数量和图形模型的残差成功时，样本量是足够的，相对于尺寸。
We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis and random effects models. We propose a Bayesian method of estimating the covariance matrices by representing the covariance model in the form of a factor model with unknown number of latent factors. We introduce binary indicators for factor selection and rank estimation for the low rank component combined with a Bayesian lasso method for the sparse component estimation. Simulation studies show that our method can recover the rank as well as the sparsity of the two components respectively. We further extend our method to a graphical factor model where the graphical model of the residuals as well as selecting the number of factors is of interest. We employ a hyper-inverse Wishart prior for modeling decomposable graphs of the residuals, and a Bayesian graphical lasso selection method for unrestricted graphs. We show through simulations that the extended models can recover both the number of latent factors and the graphical model of the residuals successfully when the sample size is sufficient relative to the dimension.