A Generalized Kernel Approach to Structured Output Learning

Abstract

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) approach to this problem using operator-valued kernels. Our formulation overcomes the two main limitations of the original KDE approach, namely the decoupling between outputs in the image space and the inability to use a joint feature space. We then propose a covariance-based operator-valued kernel that allows us to take into account the structure of the kernel feature space. This kernel operates on the output space and only encodes the interactions between the outputs without any reference to the input space. To address this issue, we introduce a variant of our KDE method based on the conditional covariance operator that in addition to the correlation between the outputs takes into account the effects of the input variables. Finally, we evaluate the performance of our KDE approach using both covariance and conditional covariance kernels on three structured output problems, and compare it to the state-of-the art kernel-based structured output regression methods.