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Reconstruction of interaction network between random events is a criticalproblem arising from statistical physics and politics to sociology, biology,and psychology, and beyond. The Ising model lays the foundation for thisreconstruction process, but finding the underlying Ising model from the leastamount of observed samples in a computationally efficient manner has beenhistorically challenging for half a century. By using the idea of sparsitylearning, we present a approach named SIMPLE that has a dominant samplecomplexity from theoretical limit. Furthermore, a tuning-free algorithm isdeveloped to give a statistically consistent solution of SIMPLE in polynomialtime with high probability. On extensive benchmarked cases, the SIMPLE approachprovably reconstructs underlying Ising models with global optimality. Theapplication on the U.S. senators voting in the last six congresses reveals thatboth the Republicans and Democrats noticeably assemble in each congresses;interestingly, the assembling of Democrats is particularly pronounced in thelatest congress.

A SIMPLE Approach to Provably Reconstruct Ising Model with Global Optimality