{"type":"ScholarlyArticle","title":"Sampling for Approximate Maximum Search in Factorized Tensor","authors":[{"name":"Zhi Lu","slug":"zhi-lu","given":"Zhi","family":"Lu","affiliation":"School of Electronic Engineering University of Electronic Science and Technology of China"},{"name":"Yang Hu","slug":"yang-hu","given":"Yang","family":"Hu","affiliation":"School of Electronic Engineering University of Electronic Science and Technology of China"},{"name":"Bing Zeng","slug":"bing-zeng","given":"Bing","family":"Zeng","affiliation":"School of Electronic Engineering University of Electronic Science and Technology of China"}],"abstract":"Factorization models have been extensively used for recovering the missing entries of a matrix or tensor. However, directly computing all of the entries using the learned factorization models is prohibitive when the size of the matrix/tensor is large. On the other hand, in many applications, such as collaborative filtering, we are only interested in a few entries that are the largest among them. In this work, we propose a sampling-based approach for finding the top entries of a tensor which is decomposed by the CANDECOMP/PARAFAC model. We develop an algorithm to sample the entries with probabilities proportional to their values. We further extend it to make the sampling proportional to the $k$-th power of the values, amplifying the focus on the top ones. We provide theoretical analysis of the sampling algorithm and evaluate its performance on several real-world data sets. Experimental results indicate that the proposed approach is orders of magnitude faster than exhaustive computing. When applied to the special case of searching in a matrix, it also requires fewer samples than the other state-of-the-art method.","doi":"10.24963/ijcai.2017/334","url":"https://ijcai.org/proceedings/2017/334","pdf":"https://ijcai.org/proceedings/2017/0334.pdf","markdown":"https://ijcai.org/proceedings/2017/334.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/334","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning A-R","track":"Main track","number":334,"pages":{"first":2400,"last":2406},"keywords":["Multidisciplinary Topics and Applications: Personalization and User Modeling","Machine Learning: Data Mining","Combinatorial & Heuristic Search: Combinatorial search/optimisation"],"videos":[],"references":[{"position":1,"raw":"[Acar et al., 2009] Evrim Acar, Daniel M Dunlavy, and Tamara G. 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