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.

我们考虑从数据联合估计多个相关的零均值高斯分布的问题。我们建议使用Laplacian正则化分层模型拟合来共同估计这些协方差矩阵，其中包括每个协方差矩阵的损失和正则项，以及一个鼓励不同协方差矩阵接近的项。该方法从相邻的协方差中“借用强度”以改善其估计。使用精心挑选的超参数，此类模型可以表现出色，尤其是在数据量较低的情况下。我们提出了一种可解决大型问题的分布式方法，并举例说明了该方法在财务，雷达信号处理和天气预报方面的功效。