Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models
Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models
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DOI：
10.1103/physrevlett.112.070603
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发表时间：
2014-02-20
影响因子：
8.6
通讯作者：
Ricci-Tersenghi, Federico
中科院分区：
文献类型：
--
作者：
Decelle, Aurelien;Ricci-Tersenghi, Federico
在这封信中，我们提出了一种新的方法来推断的拓扑结构的相互作用网络的成对模型与伊辛变量。通过在高温下使用伪电感耦合法（PLM），通常可以区分零和非零耦合，因为两组之间有一个明显的间隙。然而，在较低的温度下，PLM的有效性要低得多，结果取决于主观选择，例如l（1）正则化子的值和将非零耦合与零耦合分开的阈值。我们介绍了一个抽取过程的基础上的PLM递归设置为零的不太重要的耦合，直到相关的耦合被删除的伪随机信号的变化。新方法是完全自动化的，不需要用户的任何主观选择。数值试验已经进行了广泛的一类伊辛模型，具有不同的拓扑结构（从随机图到有限维晶格）和不同的耦合（稀释铁磁体在一个领域和自旋玻璃）。这些数值结果表明，新算法的性能优于标准PLM。
In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the l(1) regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM.