Adaptive Sample Sharing for Linear Regression

Abstract: In many business settings, task-specific labeled data are scarce or costly to obtain, which limits supervised learning on a specific task. To address this challenge, we study sample sharing in the case of ridge regression: leveraging an auxiliary data set while explicitly protecting against negative transfer. We introduce a principled, data-driven rule that decides how many samples from an auxiliary dataset to add to the target training set. The rule is based on an estimate of the transfer gain i.e. the marginal reduction in the predictive error. Building on this estimator, we derive finite-sample guaranties: under standard conditions, the procedure borrows when it improves parameter estimation and abstains otherwise. In the Gaussian feature setting, we analyze which data set properties ensure that borrowing samples reduces the predictive error. We validate the approach in synthetic and real datasets, observing consistent gains over strong baselines and single-task training while avoiding negative transfer.