Optimal structure and parameter learning of Ising models.
Optimal structure and parameter learning of Ising models.
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DOI：
10.1126/sciadv.1700791
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发表时间：
2018-03
期刊：
影响因子：
13.6
通讯作者：
Chertkov M
中科院分区：
文献类型：
--
作者：
Lokhov AY;Vuffray M;Misra S;Chertkov M
任意的伊辛模型可以精确地从使用信息论最优数据量的观测中恢复。从二值样本中重建伊辛模型的结构和参数是一个在许多学科中具有实际重要性的问题，从统计物理学和计算生物学到图像处理和机器学习。研究界的重点转向开发通用的重建算法，这些算法既计算效率高，又需要最少的昂贵数据。本文引入了一种新的方法——交互筛选法，利用局部优化问题精确估计模型参数。可以证明，该算法以信息论最优的样本数量实现了完美的图结构恢复，特别是在已知最难学习的低温状态下。通过对具有不同类型相互作用的各种拓扑结构的综合Ising模型以及D-Wave量子计算机产生的实际数据进行广泛的数值测试，评估了相互作用筛选的有效性。该研究表明，相互作用筛选方法是一种精确、易于处理和最优的技术，可以普遍解决逆伊辛问题。
An arbitrary Ising model can be exactly recovered from observations using an information-theoretically optimal amount of data. Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. We introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, which is known to be the hardest for learning. The efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. This study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.
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