Abstract:
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We propose Partial Correlation Screening (PCS) as a new row-wise estimation approach to estimating sparse precision matrices. To estimate each row of the precision matrix, PCS employs a fast Screen and Clean algorithm, where it iteratively uses the partial correlation as the screening statistic. We apply PCS to two gene microarray data sets ($(p, n) = (8491, 181)$ and $(10237, 157)$), where PCS outputs a reasonable estimate of the precision matrix in $6.3$ and $9.6$ minutes, respectively. Higher Criticism Thresholding (HCT) is a modern a adaption of Fisher's LDA. Combining HCT with either PCS or the glasso gives rise to two new classifiers, HCT-PCS and HCT-glasso. For both data sets, the classification errors of HCT-PCS are much smaller than those of the HCT-glasso, suggesting PCS have a more reasonable estimate of the precision matrix than the glasso. Compared to more popular classifiers such as SVM and Rand Forest, HCT-PCS not only is competitive in classification errors, but also enjoys interesting theoretical properties the other two methods do not have.
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