Sample-Efficient L0-L2 Constrained Structure Learning of Sparse Ising Models

We consider the problem of learning underlying graph a sparse Ising model with p nodes from n i.i.d. samples. The most recent and best performing approaches combine an empirical loss (the logistic regression or interaction screening loss) regularizer (an L1 penalty constraint). This results in convex that can be solved separately for each node graph. In this work, we leverage cardinality constraint L0 norm, which is known to properly induce sparsity, further it L2 norm better non-zero coefficients. show our proposed estimators achieve improved sample complexity, both (a) theoretically, by reaching new state-of-the-art upper bounds recovery guarantees, (b) empirically, showing sharper phase transitions between poor full topologies studied literature, when compared their L1-based methods.