Relevance Singular Vector Machine for low-rank matrix sensing
This work addresses matrix reconstruction problems for applications like recommendation systems or data imputation, but it appears incremental as it builds on existing Bayesian and low-rank methods.
The authors tackled low-rank matrix reconstruction by developing a new Bayesian inference method called Relevance Singular Vector Machine (RSVM), which uses priors on singular vectors to promote low rank and includes a computationally efficient approximation, and they demonstrated its performance numerically on matrix completion and reconstruction problems.
In this paper we develop a new Bayesian inference method for low rank matrix reconstruction. We call the new method the Relevance Singular Vector Machine (RSVM) where appropriate priors are defined on the singular vectors of the underlying matrix to promote low rank. To accelerate computations, a numerically efficient approximation is developed. The proposed algorithms are applied to matrix completion and matrix reconstruction problems and their performance is studied numerically.