Parametric Task Learning
Ichiro Takeuchi, Tatsuya Hongo, Masashi Sugiyama, Shinichi Nakajima · 2013
We introduce an extended formulation of multi-task learning (MTL) called para-metric task learning (PTL) that can systematically handle infinitely many tasks parameterized by a continuous parameter. Our key finding is that, for a certain class of PTL problems, the path of the optimal task-wise solutions can be repre-sented as piecewise-linear functions of the continuous task parameter. Based on this fact, we employ a parametric programming technique to obtain the common shared representation across all the continuously parameterized tasks. We show that our PTL formulation is useful in various scenarios such as learning under non-stationarity, cost-sensitive learning, and quantile regression. We demonstrate the advantage of our approach in these scenarios. 1