{"type":"ScholarlyArticle","title":"Accelerated Inexact Soft-Impute for Fast Large-Scale Matrix Completion","authors":[{"name":"Quanming Yao","slug":"quanming-yao","given":"Quanming","family":"Yao","affiliation":""},{"name":"James T. Kwok","slug":"james-t-kwok","given":"James T.","family":"Kwok","affiliation":""}],"abstract":"Matrix factorization tries to recover a low-rank matrix from limited observations. A state-of-the art algorithm is the Soft-Impute, which exploits a special “sparse plus low-rank” structure of the matrix iterates to allow efficient SVD in each iteration. Though Soft-Impute is also a proximal gradient algorithm, it is generally believed thatacceleration techniques are not useful and will destroy the special structure. In this paper, we show that Soft-Impute can indeed be accelerated without compromising the “sparse plus low-rank” structure. To further reduce the per-iteration time complexity, we propose an approximate singular value thresholding scheme based on the power method.Theoretical analysis shows that the proposed algorithm enjoys the fast O(1/T 2) convergence rate of accelerated proximal gradient algorithms. Extensive experiments on both synthetic and large recommendation data sets show that the proposed algorithm is much faster than Soft-Impute and other state-of-the-art matrix completion algorithms.","doi":null,"url":"https://ijcai.org/proceedings/2015/562","pdf":"https://ijcai.org/proceedings/2015/0562.pdf","markdown":"https://ijcai.org/proceedings/2015/562.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/562","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Special Track on Machine Learning","track":"Special Track on Machine Learning","number":562,"pages":{"first":4002,"last":4007},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}