# Spectral Differential Network Analysis for High-Dimensional Time Series

arXiv: https://arxiv.org/abs/2412.07905 · HTML: https://mlsanity.com/paper/2412.07905/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 36 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 10 of 10)

- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Modeling Shared Responses in Neuroimaging Studies through MultiView ICA](https://mlsanity.com/paper/2006.06635/) (2020)
- [Multivariate Convolutional Sparse Coding for Electromagnetic Brain Signals](https://mlsanity.com/paper/1805.09654/) (2018)
- [Differential Network Analysis via the Lasso Penalized D-Trace Loss](https://mlsanity.com/paper/1511.09188/) (2015)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Spectral Analysis of High-dimensional Time Series](https://mlsanity.com/paper/1810.11223/) (2018)
- [Differential Network Analysis: A Statistical Perspective](https://mlsanity.com/paper/2003.04235/) (2020)
- [Large Spectral Density Matrix Estimation by Thresholding](https://mlsanity.com/paper/1812.00532/) (2018)
- [Regularized Estimation of Sparse Spectral Precision Matrices](https://mlsanity.com/paper/2401.11128/) (2024)
- [Direct estimation of differential Granger causality between two high-dimensional time series](https://mlsanity.com/paper/2109.07609/) (2021)

## Built on by (most cited first, 1 of 1)

- [Latent Factor Point Processes for Patient Representation in Electronic Health Records](https://mlsanity.com/paper/2508.20327/) (2025)

## Abstract (arXiv)

Spectral networks derived from multivariate time series data arise in many domains, from brain science to Earth science. Often, it is of interest to study how these networks change under different conditions. For instance, to better understand epilepsy, it would be interesting to capture the changes in the brain connectivity network as a patient experiences a seizure, using electroencephalography data. A common approach relies on estimating the networks in each condition and calculating their difference. Such estimates may behave poorly in high dimensions as the networks themselves may not be sparse in structure while their difference may be. We build upon this observation to develop an estimator of the difference in inverse spectral densities across two conditions. Using an L1 penalty on the difference, consistency is established by only requiring the difference to be sparse. We illustrate the method on synthetic data experiments and on experiments with electroencephalography data.