Composable core-sets for determinant maximization: A simple near-optimal algorithm
Name
1907.03197.pdf
Description
Accepted version
Size
780.67 KB
Format
Adobe PDF
Checksum (MD5)
b9f306cffa86b002a298bad01d66e57e
Author(s)
Indyk, Piotr
Date Issued
June 2019
Journal
36th International Conference on Machine Learning, ICML 2019
Publisher
International Machine Learning Society (IMLS)
Citation
Indyk, Piotr et al. “Composable core-sets for determinant maximization: A simple near-optimal algorithm.” Paper presented at the 36th International Conference on Machine Learning, ICML 2019, Long Beach CA, Sun June 9 - 15, 2019, International Machine Learning Society (IMLS) © 2019 The Author(s)
Version
Author's final manuscript
Abstract
"Composable core-sets" are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also be cast as the MAP inference task for determinantal point processes, that have recently gained a lot of interest for modeling diversity and fairness. The problem was recently studied in (Indyk et al., 2018), where they designed composable core-sets with the optimal approximation bound of Õ(k)k. On the other hand, the more practical Greedy algorithm has been previously used in similar contexts. In this work, first we provide a theoretical approximation guarantee of O(Ck2 ) for the Greedy algorithm in the context of composable core-sets; Further, we propose to use a Local Search based algorithm that while being still practical, achieves a nearly optimal approximation bound of O(k)2k; Finally, we implement all three algorithms and show the effectiveness of our proposed algorithm on standard data sets.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://proceedings.mlr.press/v97/mahabadi19a.html
