Composable Coresets for Determinant Maximization: A Simple NearOptimal Algorithm
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:42544263, 2019.
Abstract
“Composable coresets” are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable coresets 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 \cite{indyk2018composable}, where they designed composable coresets with the optimal approximation bound of $O(k)^k$. 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 $C^{k^2}$ for the Greedy algorithm in the context of composable coresets; 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.
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