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With the advent of high-throughput sequencing, an efficient computing strategy is required to deal with large genomic data sets. The challenge of estimating a large precision matrix has garnered substantial research attention for its direct application to discriminant analyses and graphical models. Most existing methods either use a lasso-type penalty that may lead to biased estimators or are computationally intensive, which prevents their application to very large graphs.
We propose using an L0 penalty to estimate an ultra-large precision matrix (scalnetL0). We apply scalnetL0 to RNA-seq data from breast cancer patients represented in The Cancer Genome Atlas (TCGA) and find improved accuracy of classifications for survival times. The estimated precision matrix provides information about a large-scale co-expression network in breast cancer. Simulation studies demonstrate that scalnetL0 provides more accurate and efficient estimators, yielding shorter CPU time and less Frobenius loss on sparse learning for large-scale precision matrix estimation.
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