Daniel J. Williams, Leyang Wang, Qizhen Ying et al.
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.