We show that a method based on logistic regression, using all the data,
solves the inverse Ising problem far better than mean-field calculations
relying only on sample pairwise correlation functions, while still
computationally feasible for hundreds of nodes. The largest improvement in
reconstruction occurs for strong interactions. Using two examples, a diluted
Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that
interaction topologies can be recovered from few samples with good accuracy and
that the use of l1-regularization is beneficial in this process, pushing
inference abilities further into low-temperature regimes.Comment: 5 pages, 2 figures. Accepted versio