  We develop a new collaborative filtering (CF) method that combines both
previously known users' preferences, i.e. standard CF, as well as product/user
attributes, i.e. classical function approximation, to predict a given user's
interest in a particular product. Our method is a generalized low rank matrix
completion problem, where we learn a function whose inputs are pairs of vectors
-- the standard low rank matrix completion problem being a special case where
the inputs to the function are the row and column indices of the matrix. We
solve this generalized matrix completion problem using tensor product kernels
for which we also formally generalize standard kernel properties. Benchmark
experiments on movie ratings show the advantages of our generalized matrix
completion method over the standard matrix completion one with no information
about movies or people, as well as over standard multi-task or single task
learning methods.
