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 $l_1$ regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.

• Received 29 September 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.090201