Fitting Laplacian Regularized Stratified Gaussian Models
This work addresses the challenge of estimating related covariance matrices in data-scarce scenarios for applications like finance and weather forecasting, representing an incremental improvement over existing methods.
The paper tackles the problem of jointly estimating multiple related zero-mean Gaussian distributions from data by proposing a Laplacian regularized stratified model fitting method, which improves estimates by borrowing strength from neighboring covariances, especially in low data regimes, and demonstrates efficacy in finance, radar signal processing, and weather forecasting.
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.