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arXiv · 2310.09257

Reconstruct Ising Model with Global Optimality via SLIDE

Xuanyu Chen·Jin Zhu·Junxian Zhu·Xueqin Wang·Heping Zhang
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Abstract

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.

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Xuanyu Chen, Jin Zhu, Junxian Zhu, Xueqin Wang, Heping Zhang. 2023-10-13. Reconstruct Ising Model with Global Optimality via SLIDE. https://arxiv.org/abs/2310.09257

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