Faster solutions of the inverse pairwise Ising problem

Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes. Finding these models requires us to solve an inverse problem: given experimentally measured expectation values, what are the parameters of the underlying Hamiltonian? This problem sits at the intersection of statistical physics and machine learning, and we suggest that more efficient solutions are possible by merging ideas from the two fields. We use a combination of recent coordinate descent algorithms with an adaptation of the histogram Monte Carlo method, and implement these techniques to take advantage of the sparseness found in data on real neurons. The resulting algorithm learns the parameters of an Ising model describing a network of forty neurons within a few minutes. This opens the possibility of analyzing much larger data sets now emerging, and thus testing hypotheses about the collective behaviors of these networks.