Regression Transfer Learning Based on Principal Curve

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One of the basic ideas of present transfer learning algorithms is to find a common underlying representation among multiple related tasks as a bridge of transferring knowledge. Different with most transfer learning algorithms which are designed to solve classification problems, a new algorithm is proposed in this paper to solve multiple regression tasks. First, based on ”self-consistency” of principal curves, this algorithm utilizes non-parametric approach to find the principal curve passing through data sets of all tasks. We treat this curve as common-across-tasks representation. Second, the importance of every sample in target task is determined by computing the deviation from the principal curve and finally the weighted support vector regression is used to obtain a regression model. We simulate multiple related regression tasks using noisy Sinc data sets with various intensities and report experiments which demonstrate that the proposed algorithm can draw the useful information of multiple tasks and dramatically improve the performance relative to learning target task independently. Furthermore, we replace principal curve with support vector regression with model selection to find common representation and show the comparative results of these two algorithms.