Composable Core-sets for Determinant Maximization: A Simple Near-Optimal Algorithm
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"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 [IMOR'18], 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(C^k^2) 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.
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