Transfer Learning for High-Dimensional Linear Stochastic Regression

Abstract

Transfer learning (TL) is a paradigm that improves the performance of statistical tasks for the target data by leveraging information from informative source datasets. However, most existing methods are tailored to independent, light-tailed data, which may exclude critical applications involving temporal dependence or heavytailed covariates in statistical modelling, such as stock price forecasting.  In this talk, we will introduce the TL coefficient estimator for high-dimensional linear models and its rate of convergence with temporally dependent and potentially heavy-tailed covariates or error processes. Second, we propose a self-normalized (SN) type statistic and use it to screen out negative transfers, where negative transfers are source datasets that deviate significantly from the target data. Asymptotic distribution of SN statistics is established. The validity of our methods will be demonstrated through simulations and forecasting the log prices of Dow Jones Index constituents.

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