arXiv:2502.13249cond-mat.dis-nncond-mat.stat-mech2025-02被引 2

在疫情传播模型中,即使满足理想条件,仍可能出现难以推断的复杂结构。

Evidence of Replica Symmetry Breaking under the Nishimori conditions in epidemic inference on graphs

  • 通过几何化患者零号模型,研究疫情推断中的后验分布特性。
  • 在Nishimori条件下发现反常的对称性破缺现象,破坏传统认知。
  • 适用于统计物理与复杂网络推断的研究者,尤其关注贝叶斯推理困境。

在贝叶斯推断中,从数据计算后验分布通常非常困难,常需使用均值场近似或蒙特卡洛马尔可夫链等数值方法。由于后验是高度相关变量上的高维分布,可能经历著名的复本对称性破缺相变。一旦发生,多数均值场方法和几乎所有蒙特卡洛方案都无法合理逼近后验及其边缘分布。人们普遍认为,当数据由已知先验和似然生成时——即满足所谓的Nishimori条件——复本对称性将被保证。本文通过一个简单几何模型(可视为高传染性流行病中患者零号的恢复问题),提供反例表明:在Nishimori条件下,复本对称性依然可能被打破。我们通过计算复本对称腔方法向一步复本对称性破缺相的不稳定性,得出该现象存在的证据。其根源可能在于流行病模型中出现的相关无序效应。

原文摘要 · Abstract (English)

In Bayesian inference, computing the posterior distribution from the data is typically a non-trivial problem, which usually requires approximations such as mean-field approaches or numerical methods, like the Monte Carlo Markov Chain. Being a high-dimensional distribution over a set of correlated variables, the posterior distribution can undergo the notorious replica symmetry breaking transition. When it happens, several mean-field methods and virtually every Monte Carlo scheme can not provide a reasonable approximation to the posterior and its marginals. Replica symmetry is believed to be guaranteed whenever the data is generated with known prior and likelihood distributions, namely under the so-called Nishimori conditions. In this paper, we break this belief, by providing a counter-example showing that, under the Nishimori conditions, replica symmetry breaking arises. Introducing a simple, geometrical model that can be thought of as a patient zero retrieval problem in a highly infectious regime of the epidemic Susceptible-Infectious model, we show that under the Nishimori conditions, there is evidence of replica symmetry breaking. We achieve this result by computing the instability of the replica symmetric cavity method toward the one step replica symmetry broken phase. The origin of this phenomenon -- replica symmetry breaking under the Nishimori conditions -- is likely due to the correlated disorder appearing in the epidemic models.

贝叶斯推断复本对称性流行病建模

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