Active learning and search on low-rank matrices

Collaborative prediction is a powerful technique, useful in domains from recommender systems to guiding the scien-tific discovery process. Low-rank matrix factorization is one of the most powerful tools for collaborative prediction. This work presents a general approach for active collabora-tive prediction with the Probabilistic Matrix Factorization model. Using variational approximations or Markov chain Monte Carlo sampling to estimate the posterior distribution over models, we can choose query points to maximize our un-derstanding of the model, to best predict unknown elements of the data matrix, or to find as many “positive ” data points as possible. We evaluate our methods on simulated data, and also show their applicability to movie ratings prediction and the discovery of drug-target interactions