Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties

Understand

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs).

• The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.
• When the functions in the TP-RKHS are defined on the Cartesian product of finite discrete sets, in particular, our main problem formulation admits as a special case existing tensor completion problems.
• Other special cases include transfer learning with multimodal side information and multilinear multitask learning.