High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching

TL;DR

This paper introduces a novel method for directly estimating the time derivatives of parameters in high-dimensional exponential family models using time score matching, enabling efficient inference of dynamic structures.

Contribution

It proposes a new approach that estimates differential parameters directly, avoiding separate model fitting at each time point, with theoretical guarantees and practical validation.

Findings

Consistent estimation of differential parameters in high dimensions.

Finite-sample normality of the debiased estimator.

Effective inference of dynamic graphical models.

Abstract

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.