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• W2962838391 abstract "We propose Partial Correlation Screening (PCS) as a new row-by-row approach to estimating a large precision matrix $Omega$. To estimate the $i$-th row of $Omega$, $1 leq i leq p$, PCS uses a Screen step and a Clean step. In the Screen step, PCS recruits a (small) subset of indices using a stage-wise algorithm, where in each stage, the algorithm updates the set of recruited indices by adding the index $j$ that has the largest (in magnitude) empirical partial correlation with $i$. In the Clean step, PCS re-investigates all recruited indices and use them to reconstruct the $i$-th row of $Omega$. PCS is computationally efficient and modest in memory use: to estimate a row of $Omega$, it only needs a few rows (determined sequentially) of the empirical covariance matrix. This enables PCS to execute the estimation of a large precision matrix (e.g., $p=10K$) in a few minutes, and open doors to estimating much larger precision matrices. We use PCS for classification. Higher Criticism Thresholding (HCT) is a recent classifier that enjoys optimality, but to exploit its full potential in practice, one needs a good estimate of the precision matrix $Omega$. Combining HCT with any approach to estimating $Omega$ gives a new classifier: examples include HCT-PCS and HCT-glasso. We have applied HCT-PCS to two large microarray data sets ($p = 8K$ and $10K$) for classification, where it not only significantly outperforms HCT-glasso, but also is competitive to the Support Vector Machine (SVM) and Random Forest (RF). The results suggest that PCS gives more useful estimates of $Omega$ than the glasso. We set up a general theoretical framework and show that in a broad context, PCS fully recovers the support of $Omega$ and HCT-PCS yields optimal classification behavior. Our proofs shed interesting light on the behavior of stage-wise procedures." @default.
• W2962838391 created "2019-07-30" @default.
• W2962838391 creator A5075757275 @default.
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• W2962838391 date "2016-10-01" @default.
• W2962838391 modified "2023-09-27" @default.
• W2962838391 title "Partial correlation screening for estimating large precision matrices, with applications to classification" @default.
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• W2962838391 doi "https://doi.org/10.1214/15-aos1392" @default.
• W2962838391 hasPublicationYear "2016" @default.
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