Sparse Tensor Decomposition for Multi-task Interaction Selection

Multi-task learning aims to improve the generalization performance of related tasks based on simultaneous learning where prediction models share information. Recently, identifying significant feature interaction attracts more interests because of its practical importance. We propose a second-order interaction method for multi-task learning, which identifies significant linear and interaction terms. We develop a sparse tensor decomposition based on a feature augmentation and a symmetrization trick to express the prediction models of related tasks as the linear combinations of the shared parameters. We show that the proposed method could generate diverse relationships between linear and interaction terms. In minimizing the resulting multiconvex objective function, we select an initial value by deriving unbiased estimators and proposing a tensor decomposition. Experiments on synthetic and benchmark datasets demonstrate the effectiveness of the proposed method.