Learning Multiple Tasks using Manifold Regularization

We present a novel method for multitask learning (MTL) based on {\it manifold regularization}: assume that all task parameters lie on a manifold. This is the generalization of a common assumption made in the existing literature: task parameters share a common {\it linear} subspace. One proposed method uses the projection distance from the manifold to regularize the task parameters. The manifold structure and the task parameters are learned using an alternating optimization framework. When the manifold structure is fixed, our method decomposes across tasks which can be learnt independently. An approximation of the manifold regularization scheme is presented that preserves the convexity of the single task learning problem, and makes the proposed MTL framework efficient and easy to implement. We show the efficacy of our method on several datasets.