从不稳定采样中恢复真实离散分布，突破传统采样瓶颈
Discrete distributions are learnable from metastable samples
- 利用条件概率平均接近真实分布的特性，从亚稳态样本中重建模型
- 即使在KL散度大的情况下，仍能准确学习伊辛模型的参数与结构
- 适用于物理模拟中难以跳出亚稳态的复杂系统建模
物理启发的随机动力学广泛用于高维分布采样，但采样器常陷入亚稳态，导致实际采样分布与目标稳态分布显著偏离。本文严格证明：对于满足强亚稳性条件的多变量离散分布，其单变量条件概率在平均意义上与真实稳态分布极为接近，即便两者在全局度量（如KL散度）下相去甚远。因此，即使样本来自受限状态空间，仍可使用条件似然估计器有效学习真实模型。将该理论扩展至伊辛模型，给出了严格的参数与结构学习保证。最后，在高字母自旋玻璃模型上数值验证了该现象。
原文摘要 · Abstract (English)
Physically motivated stochastic dynamics are widely used to sample from high-dimensional distributions. However, such samplers often get trapped in metastable states, approximately sampling from a distribution that differs significantly from the desired stationary state. We rigorously show that for multivariable discrete distributions, the true stationary model can nevertheless be recovered from these metastable samples. This relies on a fundamental observation: for distributions satisfying a strong metastability condition, their single-variable conditional probabilities are on average extremely close to those of the true stationary distribution. This remains true even when the two distributions are far apart under global metrics such as Kullback-Leibler divergence. Consequently, we can effectively learn the true model using a conditional-likelihood estimator even when the samples are drawn from a restricted state space. Extending these general results to Ising models, we prove rigorous parameter and structure learning guarantees. Finally, we demonstrate this phenomenon numerically on higher-alphabet spin glass models.
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