推断在与神经网络先验传播过程中的推断
Davide Ghio1, Fabrizio Boncoraglio2, Lenka Zdeborová2
1École Polytechnique Fédérale de Lausanne, Information, Learning and Physics Laboratory, (EPFL), Lausanne, Switzerland.
Physical review. E
|February 20, 2026
概括
我们介绍了一个神经网络模型来推断流行病状态,将节点共变量纳入更现实的初始条件. 这种方法增强了状态恢复,尽管阶段过渡可以创建统计到计算的差距.
科学领域:
- 复杂的系统复杂的系统.
- 统计推理 统计推理
- 机器学习 机器学习
背景情况:
- 图表上的随机过程模拟流行病,但通常假设随机的初始状态.
- 现实世界的系统具有影响初始状态的节点共变量,这是一个在推理中经常被忽视的因素.
研究的目的:
- 在图表上模拟随机过程的初始状态作为节点共变量的神经网络函数.
- 开发一个贝叶斯推理框架,利用过程动态和共变量信息.
- 分析神经网络前置对状态和轨迹恢复的影响.
主要方法:
- 一种混合的信念传播和近似信息传递 (BP-AMP) 算法得到了推导.
- 该算法将传播动态与节点共变量信息集成在一起.
- 性能与仅使用扩散或仅使用共变量信息的方法进行了比较.
主要成果:
- 拟议的模型通过结合共变量信息来增强初始状态和传播轨迹的恢复.
- 在一些方案中观察到第一阶段过渡,特别是在Rademacher分布的神经网络权重的情况下.
- 一个统计到计算的差距出现了,在那里完美的恢复在理论上是可能的,但在计算上是无法实现的.
结论:
- 基于节点共变量的神经网络先验集成可以改善对图形上的随机过程的推理.
- 阶段过渡和由此产生的统计与计算差距对准确的状态估计提出了挑战.
- 该BP-AMP算法提供了一个强大的方法来处理复杂的推理问题与集成的共变量信息.
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