Recent Results on High-dimensional Robust Matrix Regression

With the advent of the big data era, we are facing with more and more complex data. In practice, however, it is not clear whether the data is heavily tailed or contains outliers. In this talk, we mainly focus on the robust Huber matrix regression (HMR) model in high-dimensional setting. Considering the data structure, such as low-rank, collinearity and row-sparsity, we propose nuclear norm regularized HMR model, matrix elastic-net regularized HMR model and row-elastic-net regularized HMR model. For these three models, we prove the property of resistance to outliers and derive the non-asymptotic risk bound. For the last two models, we show the grouping effect property which can deal with collinearity. In terms of optimization algorithm, we design accelerated proximal (sub-)gradient methods and give the iteration complexity.