  Maximum entropy methods provide a principled path connecting measurements of
neural activity directly to statistical physics models, and this approach has
been successful for populations of $N\sim 100$ neurons. As $N$ increases in new
experiments, we enter an undersampled regime where we have to choose which
observables should be constrained in the maximum entropy construction. The best
choice is the one that provides the greatest reduction in entropy, defining a
"minimax entropy" principle. This principle becomes tractable if we restrict
attention to correlations among pairs of neurons that link together into a
tree; we can find the best tree efficiently, and the underlying statistical
physics models are exactly solved. We use this approach to analyze experiments
on $N\sim 1500$ neurons in the mouse hippocampus, and show that the resulting
model captures the distribution of synchronous activity in the network.
