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"NIPS Neural Information Processing Systems 8-11th December 2014, Montreal, Canada",,, "Paper ID:","1466" "Title:","Multitask learning meets tensor factorization: task imputation via convex optimization" Current Reviews First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. In this paper, the authors study the problem of learning a tensor for the purpose of linear multi-task learning. The authors propose a new weighted version of a previously proposed tensor norm (called latent trace norm) and show that the introduced rescaling yields better bounds on the excess risk as well as improved recovery performance on some datasets. The paper is well written and organized, and the proposed rescaling can potentially have a significant impact in practice, although a more extensive experimental evaluation would have been desirable. The technical results seem to be appropriate and correctly proven.

We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method of multipliers, which is computationally efficient when the number of training samples is moderate. We then theoretically derive an excess risk bound for each tensor norm and clarify their behavior. Finally, we perform extensive experiments using simulated and real data and demonstrate the superiority of tensor-based learning methods over vector- and matrix-based learning methods.