Probabilistic Low-Rank Matrix Completion with Adaptive Spectral Regularization Algorithms

Adrien Todeschini (1, 2, 3) , Francois Caron (4) , Marie Chavent (2, 3)

1 ALEA - Advanced Learning Evolutionary Algorithms
2 IMB - Institut de Mathématiques de Bordeaux
3 CQFD - Quality control and dynamic reliability
4 Department of Statistics [Oxford]

We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an Expectation-Maximization algorithm to obtain a Maximum A Posteriori estimate of the completed low rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values. The algorithm is simple to implement and can scale to large matrices. We provide numerical comparisons between our approach and recent alternatives showing the interest of the proposed approach for low rank matrix completion.

Domains: Machine Learning [stat.ML]; Methodology [stat.ME]; Computation [stat.CO]; Applications [stat.AP]

Adrien Todeschini, Francois Caron, Marie Chavent. Probabilistic Low-Rank Matrix Completion with Adaptive Spectral Regularization Algorithms. NIPS - The Neural Information Processing Systems Conference, The Neural Information Processing Systems (NIPS) Foundation, Inc., Dec 2013, South Lake Tahoe, United States. pp.845-853. ⟨hal-01025508⟩