直接学习参数随时间的变化率，提升高维动态模型推断效率
High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching
- 将时变参数导数建模为指数族的线性函数，通过时间得分匹配直接估计
- 在高维情况下证明了正则化得分匹配的一致性与去偏估计的有限样本正态性
- 适用于结构随时间变化的高维图模型，适合数据流或动态系统分析者
本文研究时变参数概率模型中的微分推断问题，如结构随时间变化的图模型。不同于在每个时间点分别估计高维模型再分析变化，本文直接学习参数的微分（即时间导数）。核心思想是将指数族模型的时间得分函数视为微分参数的线性模型，从而实现直接估计。采用时间得分匹配方法估计参数导数，并证明了正则化得分匹配目标的一致性，以及在高维设置下去偏估计的有限样本正态性。该方法在模拟和真实数据集上均有效推断出高维图模型的微分结构。实验代码见：https://github.com/Leyangw/tsm。
原文摘要 · Abstract (English)
This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time point and estimating changes later, we directly learn the differential parameter, i.e., the time derivative of the parameter. The main idea is treating the time score function of an exponential family model as a linear model of the differential parameter for direct estimation. We use time score matching to estimate parameter derivatives. We prove the consistency of a regularized score matching objective and demonstrate the finite-sample normality of a debiased estimator in high-dimensional settings. Our methodology effectively infers differential structures in high-dimensional graphical models, verified on simulated and real-world datasets. The code reproducing our experiments can be found at: https://github.com/Leyangw/tsm.
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