用伯恩斯坦归一化流统一建模非线性随机系统，实现精确推理。
Universal Learning of Stochastic Dynamics for Exact Belief Propagation using Bernstein Normalizing Flows
- 结合归一化流与伯恩斯坦多项式，兼具表达力与解析可计算性。
- 在非加性、非高斯噪声的强非线性系统中优于现有数据驱动方法。
- 适合需要精确概率推理的复杂动态系统建模任务。
预测随机系统未来状态分布（即信念传播）是不确定性推理的基础。然而，非线性动态常使解析信念传播不可行，需依赖近似方法。当系统模型未知且需从数据学习时，关键问题是：能否学习一种既能普遍逼近一般非线性随机动态，又能支持解析信念传播的模型？本文建立了满足这两项性质的模型类的理论基础。所提方法将归一化流在密度估计中的表达力与伯恩斯坦多项式的解析可计算性相结合。实证结果表明，该学习模型在高度非线性系统（含非加性、非高斯噪声）的信念传播上，优于现有最先进数据驱动方法。
原文摘要 · Abstract (English)
Predicting the distribution of future states in a stochastic system, known as belief propagation, is fundamental to reasoning under uncertainty. However, nonlinear dynamics often make analytical belief propagation intractable, requiring approximate methods. When the system model is unknown and must be learned from data, a key question arises: can we learn a model that (i) universally approximates general nonlinear stochastic dynamics, and (ii) supports analytical belief propagation? This paper establishes the theoretical foundations for a class of models that satisfy both properties. The proposed approach combines the expressiveness of normalizing flows for density estimation with the analytical tractability of Bernstein polynomials. Empirical results show the efficacy of our learned model over state-of-the-art data-driven methods for belief propagation, especially for highly non-linear systems with non-additive, non-Gaussian noise.
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