Active learning for matrix completion

Matrix completion is an essential problem in modern machine learning, as it is e.g. important for the calibration of the recommendation systems. We consider the problem of matrix completion in the setting where the learner can choose where to sample. In this setting, it can be of interest to target more specifically parts of the matrix where it is discovered that the complexity is high (higher local rank), where the knowledge is limited (few sampled points), or where the noise is high. This project plans to consider first the problem of active learning for matrix completion when the matrix can be subdivided into block submatrices of small ranks that are known, and then in the more general case where this cannot be done.