Transfer Learning for High dimensional Linear Regression Prediction Estimation and Minimax Optimality

This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression models . When the set of “informative” auxiliary samples is known, an estimator and a predictor are proposed and their optimality is established . The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples . This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem . The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions . It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating the data from multiple different tissues as auxiliary tissues as auxiliary samples. It is also shown that it leads to an improved performance

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Keywords : samples - auxiliary - prediction - target - estimation -

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