Fast nonparametric matrix factorization for large-scale collaborative filtering

With the sheer growth of online user data, it becomes challenging to develop preference learning algorithms that are sufficiently flexible in modeling but also affordable in computation. In this paper we develop nonparametric matrix factorization methods by allowing the latent factors of two low-rank matrix factorization methods, the singular value decomposition (SVD) and probabilistic principal component analysis (pPCA), to be data-driven, with the dimensionality increasing with data size. We show that the formulations of the two nonparametric models are very similar, and their optimizations share similar procedures. Compared to traditional parametric low-rank methods, nonparametric models are appealing for their flexibility in modeling complex data dependencies. However, this modeling advantage comes at a computational price--it is highly challenging to scale them to large-scale problems, hampering their application to applications such as collaborative filtering. In this paper we introduce novel optimization algorithms, which are simple to implement, which allow learning both nonparametric matrix factorization models to be highly efficient on large-scale problems. Our experiments on EachMovie and Netflix, the two largest public benchmarks to date, demonstrate that the nonparametric models make more accurate predictions of user ratings, and are computationally comparable or sometimes even faster in training, in comparison with previous state-of-the-art parametric matrix factorization models.