Self-Supervised Learning for Covariance Estimation

Abstract: We consider the use of deep learning for covariance estimation. We propose to globally learn a neural network that will then be applied locally at inference time. Leveraging recent advancements in self-supervised foundational models, we train the network without any labeling by simply masking different samples and learning to predict their covariance given their surrounding neighbors. The architecture is based on the popular attention mechanism. Its main advantage over classical methods is the automatic exploitation of global characteristics without any distributional assumptions or regularization. It can be pre-trained as a foundation model and then be repurposed for various downstream tasks, e.g., adaptive target detection in radar or hyperspectral imagery.