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反向偏差是对近临界行为的Ising估计

Maximilian B Kloucek^1,2, Thomas Machon¹, Shogo Kajimura³

¹School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.

Physical review. E

|August 16, 2023

概括

反向Ising推理重建系统相互作用,但诸如伪概率最大化 (PLM) 等常见方法是有偏见的. 这种偏差,特别是在临界点附近,可以误解数据,需要进行偏差校正以进行准确的分析.

科学领域:

统计物理学的统计物理.
计算神经科学是一种计算神经科学.
机器学习是机器学习.

背景情况:

反向Ising推理旨在从观察到的相关性中重建复杂的二进制系统中的对互动.
众所周知,常见的推断方法,如伪概率最大化 (PLM),会表现出偏差.
这些偏差在关键系统中可能特别显著,可能导致对系统属性的误解.

研究的目的:

量化伪概率最大化 (PLM) 对反向Ising推理的偏差,特别是在临界点附近.
调查小样本偏差对推断模型及其接近关键性的影响.
探索并将数据驱动的偏差校正方法应用于现实数据,例如功能磁共振成像 (fMRI) 数据.

主要方法:

利用Sherrington-Kirkpatrick模型作为一个基准来系统地分析推断偏差.
在不同条件下评估伪概率最大化 (PLM) 的性能,重点关注关键模式.
开发和实施数据驱动的技术来纠正反向Ising模型中发现的偏差.

主要成果:

证明PLM中的偏差在相位边界和关键模式附近是相当大的.
显示小样本偏差导致推断模型比经验数据表明的更接近关键性.
成功地将偏差校正方法应用于功能磁共振成像 (fMRI) 数据集.

结论:

标准的反向Ising推断方法固有的偏差可以显著扭曲系统关键性的解释.
在从现实数据中推断关键性时必须小心,特别是当使用不进行偏差校正的PLM等方法时.
数据驱动偏差校正对于精确重建复杂系统中的相互作用和属性至关重要.

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