Reconstruction of interaction network between random events is a critical problem arising from statistical physics and politics to sociology, biology, and psychology, and beyond. The Ising model lays the foundation for this reconstruction process, but finding the underlying Ising model from the least amount of observed samples in a computationally efficient manner has been historically challenging for half a century. By using the idea of sparsity learning, we present a approach named SIMPLE that has a dominant sample complexity from theoretical limit. Furthermore, a tuning-free algorithm is developed to give a statistically consistent solution of SIMPLE in polynomial time with high probability. On extensive benchmarked cases, the SIMPLE approach provably reconstructs underlying Ising models with global optimality. The application on the U.S. senators voting in the last six congresses reveals that both the Republicans and Democrats noticeably assemble in each congresses; interestingly, the assembling of Democrats is particularly pronounced in the latest congress.

翻译：随机事件之间交互网络的重构是统计物理、政治学、社会学、生物学、心理学等多个领域的关键问题。伊辛模型为此重构过程奠定了理论基础，但半个世纪以来，如何以计算高效的方式从最少的观测样本中恢复潜在伊辛模型始终是历史性难题。借助稀疏学习的思想，我们提出了一种名为SIMPLE的方法，该方法在理论极限下具有主导性的样本复杂度。此外，我们开发了一种无需调参的算法，能够在多项式时间内以高概率给出SIMPLE的统计一致解。在广泛的基准测试案例中，SIMPLE方法以全局最优性可证明地重构了潜在伊辛模型。将该方法应用于美国参议员在近六届国会中的投票数据，结果显示共和党与民主党各自在每届国会中均呈现出显著聚集现象；有趣的是，民主党在最新一届国会中的聚集特征尤为突出。