The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, 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. Using sparsity learning, we present an approach named SLIDE whose sample complexity is globally optimal. Furthermore, an algorithm is developed to give a statistically consistent solution of SLIDE in polynomial time with high probability. On extensive benchmarked cases, the SLIDE approach demonstrates dominant performance in reconstructing underlying Ising models, confirming its superior statistical properties. The application on the U.S. senators voting in the six congresses reveals that both the Republicans and Democrats noticeably assemble in each congress; interestingly, the assembling of Democrats is particularly pronounced in the latest congress.

翻译：随机事件间交互网络的重构是一个源于统计物理学，并广泛存在于政治学、社会学、生物学、心理学等诸多领域的关键问题。伊辛模型为这一重构过程奠定了基础，但如何以计算高效的方式，从最少数量的观测样本中找出潜在的伊辛模型，半个世纪以来一直是个历史性难题。利用稀疏学习，我们提出了一种名为SLIDE的方法，其样本复杂度是全局最优的。此外，我们开发了一种算法，能以高概率在多项式时间内给出SLIDE的统计一致解。在广泛的基准测试案例中，SLIDE方法在重构潜在伊辛模型方面展现出卓越的性能，证实了其优越的统计特性。该方法应用于美国参议员在六届国会中的投票数据，揭示了共和党与民主党在每届国会中都表现出明显的聚集现象；有趣的是，民主党在最近一届国会中的聚集尤为显著。