# Fitting Laplacian Regularized Stratified Gaussian Models

arXiv: https://arxiv.org/abs/2005.01752 · HTML: https://mlsanity.com/paper/2005.01752/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2020.

## Built on by (most cited first, 4 of 4)

- [Covariance Prediction via Convex Optimization](https://mlsanity.com/paper/2101.12416/) (2021)
- [Exponentially Weighted Moving Models](https://mlsanity.com/paper/2404.08136/) (2024)
- [Joint Graph Learning and Model Fitting in Laplacian Regularized Stratified Models](https://mlsanity.com/paper/2305.02573/) (2023)
- [PV Fleet Modeling via Smooth Periodic Gaussian Copula](https://mlsanity.com/paper/2307.00004/) (2023)

## Abstract (arXiv)

We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss and regularization terms for each covariance matrix, and also a term that encourages the different covariances matrices to be close. This method `borrows strength' from the neighboring covariances, to improve its estimate. With well chosen hyper-parameters, such models can perform very well, especially in the low data regime. We propose a distributed method that scales to large problems, and illustrate the efficacy of the method with examples in finance, radar signal processing, and weather forecasting.