  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.
