Sparse classification: a scalable discrete optimization perspective

We formulate the sparse classification problem of n samples with p features as a binary convex optimization and propose outer-approximation algorithm to solve it exactly. For logistic regression SVM, our finds optimal solutions for in 10,000 s within minutes. On synthetic data achieves perfect support recovery large sample regime. Namely, there exists an $$n_0$$ such that takes long time find solution does not recover correct $$n0$$ .