Transfer-Learning Across Datasets with Different Input Dimensions: An Algorithm and Analysis for the Linear Regression Case

With the development of new sensors and monitoring devices, more sources of data become available to be used as inputs for machine learning models. These can on the one hand help to improve the accuracy of a model. On the other hand however, combining these new inputs with historical data remains a challenge that has not yet been studied in enough detail. In this work, we propose a transfer-learning algorithm that combines the new and the historical data, that is especially beneficial when the new data is scarce. We focus the approach on the linear regression case, which allows us to conduct a rigorous theoretical study on the benefits of the approach. We show that our approach is robust against negative transfer-learning, and we confirm this result empirically with real and simulated data.