Bayesian Matrix Completion via Adaptive Relaxed Spectral Regularization

Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization formulation. We fill this gap by presenting a novel Bayesian matrix completion method based on spectral regularization. In order to circumvent the difficulties of dealing with the orthonormality constraints of singular vectors, we derive a new equivalent form with relaxed constraints, which then leads us to design an adaptive version of spectral regularization feasible for Bayesian inference. Our Bayesian method requires no parameter tuning and can infer the number of latent factors automatically. Experiments on synthetic and real datasets demonstrate encouraging results on rank recovery and collaborative filtering, with notably good results for very sparse matrices.Comment: Accepted to AAAI 201

Kernel Methods for Collaborative Filtering

The goal of the thesis is to extend the kernel methods to matrix factorization(MF) for collaborative ltering(CF). In current literature, MF methods usually assume that the correlated data is distributed on a linear hyperplane, which is not always the case. The best known member of kernel methods is support vector machine (SVM) on linearly non-separable data. In this thesis, we apply kernel methods on MF, embedding the data into a possibly higher dimensional space and conduct factorization in that space. To improve kernelized matrix factorization, we apply multi-kernel learning methods to select optimal kernel functions from the candidates and introduce L2-norm regularization on the weight learning process. In our empirical study, we conduct experiments on three real-world datasets. The results suggest that the proposed method can improve the accuracy of the prediction surpassing state-of-art CF methods