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

arXiv: https://arxiv.org/abs/2410.10637 · HTML: https://mlsanity.com/paper/2410.10637/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Estimation of High-Dimensional Graphical Models Using Regularized Score Matching](https://mlsanity.com/paper/1507.00433/) (2015)
- [Estimating Density Models with Truncation Boundaries using Score Matching](https://mlsanity.com/paper/1910.03834/) (2019)
- [Generalized Score Matching for General Domains](https://mlsanity.com/paper/2009.11428/) (2020)
- [Estimating Time-Varying Graphical Models](https://mlsanity.com/paper/1804.03811/) (2018)
- [Direct Estimation of Differential Functional Graphical Models](https://mlsanity.com/paper/1910.09701/) (2019)
- [Two-sample inference for high-dimensional Markov networks](https://mlsanity.com/paper/1905.00466/) (2019)
- [Support Consistency of Direct Sparse-Change Learning in Markov Networks](https://mlsanity.com/paper/1407.0581/) (2014)
- [Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso](https://mlsanity.com/paper/1512.06171/) (2015)
- [Change-Point Estimation in High-Dimensional Markov Random Field Models](https://mlsanity.com/paper/1405.6176/) (2014)
- [ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models](https://mlsanity.com/paper/1502.07641/) (2015)
- [De-biased Lasso for Generalized Linear Models with A Diverging Number of Covariates](https://mlsanity.com/paper/2110.04433/) (2021)
- [Score Matching for Truncated Density Estimation on a Manifold](https://mlsanity.com/paper/2206.14668/) (2022)

## Built on by (most cited first, 2 of 2)

- [Density Ratio Estimation with Conditional Probability Paths](https://mlsanity.com/paper/2502.02300/) (2025)
- [Guiding Time-Varying Generative Models with Natural Gradients on Exponential Family Manifold](https://mlsanity.com/paper/2502.07650/) (2025)

## Abstract (arXiv)

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.