Robust multitask feature learning with adaptive Huber regressions

Abstract When data from multiple tasks have outlier contamination, existing multitask learning methods perform less efficiently. To address this issue, we propose a robust multitask feature learning method by combining the adaptive Huber regression tasks with mixed regularization. The robustification parameters can be chosen to adapt to the sample size, model dimension, and moments of the error distribution while striking a balance between unbiasedness and robustness. We consider heavy‐tailed distributions for multiple datasets that have bounded th moment for any . Our method can achieve estimation and sign recovery consistency. Additionally, we propose a robust information criterion to conduct joint inference on related tasks, which can be used for consistent model selection. Through different simulation studies and real data applications, we illustrate that the performance of the proposed model can provide smaller estimation errors and higher feature selection accuracy than the non robust multitask learning and robust single‐task methods.