Robust transfer regression with corrupted labels

In this paper, we introduce a robust transfer regression method designed to handle corrupted labels in target data, under the scenarios that the corruption affects a substantial portion of the labels and the locations of these corruptions are unknown. Theoretical analysis substantiates our approach, illustrating that the estimation error consists of three components: the first relates to the source data; the second encompasses the domain shift ; and the third captures the estimation error attributed to the corrupted vector. Our theoretical framework ensures that the proposed method surpasses estimations based solely on target data. We validate our method through numerical experiments aimed at reconstructing corrupted compressed signals. Additionally, we apply our method to analyze the association between O6-methylguanine-DNA methyltransferase (MGMT) methylation and gene expression in Glioblastoma (GBM) patients. Keywords: