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Matrix factorization with trace norm regularization is a popular approach to matrix completion and collaborative filtering. When entries of the matrix are sampled non-uniformly (which is the case for collaborative prediction), a properly weighted correction to the trace norm regularization is known to improve the performance dramatically. While the weighted trace norm regularization has been rigorously...
Matrix co-factorization involves jointly decomposing several data matrices to approximate each data matrix as a product of two factor matrices, sharing some factor matrices in the factorization. We have recently developed variational Bayesian matrix co-factorization where factor matrices are inferred by computing variational posterior distributions in the case of Gaussian likelihood with Gaussian...
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