Adaptive Reduced Rank Regression

Low rank regression has proven to be useful in a wide range of forecasting problems. However, in settings with a low signal-to-noise ratio, it is known to suffer from severe overfitting. This paper studies the reduced rank regression problem and presents algorithms with provable generalization guarantees. We use adaptive hard rank-thresholding in two different parts of the data analysis pipeline. First, we consider a low rank projection of the data to eliminate the components that are most likely to be noisy. Second, we perform a standard multivariate linear regression estimator on the data obtained in the first step, and subsequently consider a low-rank projection of the obtained regression matrix. Both thresholding is performed in a data-driven manner and is required to prevent severe overfitting as our lower bounds show. Experimental results show that our approach either outperforms or is competitive with existing baselines.