Inverse Ising inference using all the data
  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. 
Erik Aurell and Magnus Ekeberg
cond-mat.dis-nn cond-mat.stat-mech physics.data-an