  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.
