Estimation with Norm Regularization, with Applications to Climate Science

The talk will discuss recent advances in the analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, as well as application of such estimation to climate science.

Analysis of estimation error for regularized problems needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. The talk will discuss new results on all four aspects. In particular, the new results are applicable to any norm, general design matrices, including sub-Gaussian, anisotropic, and dependent samples, general convex loss functions, including least squares and generalized linear models, and both Gaussian and sub-Gaussian noise models. Gaussian width, a measure of size of sets, and associated tools play a key role in our general analysis. We show applications of the such structured/sparse estimation for multi-task learning in the context of combining climate models, with promising preliminary results.