Scalable network estimation with L 0 penalty

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 applications to very large graphs. We propose using an L 0 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 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.