Transfer learning for high-dimensional data with heavy-tailed noise: A sparse convoluted rank regression method

Transfer learning can leverage information from the source domain to improve the estimation or prediction accuracy of the target task. For the high-dimensional linear regression model with sub-Gaussian noise, so-called Trans-Lasso algorithm has been proposed to boost the learning performance on the target domain. However, such algorithm may not lead to efficient estimates when the errors are heavy-tailed. In this paper, we investigate the penalized convoluted rank regression (CRR) under the transfer learning framework, aiming to provide robust estimators when dealing with heavy-tailed noise. The convolution smoothing technique improves the smoothness of the loss function without introducing any bias. In the high-dimensional setting, we first propose a transfer learning algorithm on the penalized CRR models with known transferable sources, and establish ℓ2/ℓ1-estimation error bounds for the corresponding estimators. Besides, we propose a transferable detection method to select informative sources and also verify its consistency. At last, we demonstrate the validity and effectiveness of our proposed methods using simulated data and a real-world dataset concerning the associations among gene expressions.