We discover a screening rule for l1-regularized Ising model estimation. The simple closed-form screening rule is a necessary and sufficient condition for exactly recovering the blockwise structure of a solution under any given regularization parameters. With enough sparsity, the screening rule can be combined with various optimization procedures to deliver solutions efficiently in practice. The screening rule is especially suitable for large-scale exploratory data analysis, where the number of variables in the dataset can be thousands while we are only interested in the relationship among a handful of variables within moderate-size clusters for interpretability. Experimental results on various datasets demonstrate the efficiency and insights gained from the introduction of the screening rule.

While the field of statistical learning with sparsity [Hastie et al., 2015] has been steadily rising to

We develop methods for rapidly identifying important components of a convex optimization problem for the purpose of achieving fast convergence times.

For statistical learning in high dimension, sparse regularizations have proven useful to boost both computational and statistical efficiency.

Current numerical procedures for SLOPE, however, lack the efficiency that respective tools for the lasso enjoy, particularly in the context of estimating a complete regularization path.

Fortunately, the introduction of so-called screening rules has improved this situation remarkably.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors propose a new screening rule Slores for pre-filtering variables for logistic regression. This statement though sounds too simple and doesn't give the paper justice at all. The paper provides a rigorous and theoretically well founded derivation of a novel pre-screening rule which could in principle be extended to other settings as well. The method is also efficient compared to other safe rules that guarantee to discard only non-zero entries.