Ensemble Pruning: A Submodular Function Maximization Perspective

2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chaofeng Sha ◽  
Keqiang Wang ◽  
Xiaoling Wang ◽  
Aoying Zhou
Keyword(s):  
Submodular Function ◽  
Ensemble Pruning ◽  
Submodular Function Maximization

scholarly journals Very Fast Streaming Submodular Function Maximization

2021 ◽  
pp. 151-166
Author(s):  
Sebastian Buschjäger ◽  
Philipp-Jan Honysz ◽  
Lukas Pfahler ◽  
Katharina Morik
Keyword(s):  
Submodular Function ◽  
Submodular Function Maximization

scholarly journals Submodular Function Maximization

Tractability ◽  
2014 ◽  
pp. 71-104 ◽  
Author(s):  
Andreas Krause ◽  
Daniel Golovin
Keyword(s):  
Submodular Function ◽  
Submodular Function Maximization

scholarly journals An optimal monotone contention resolution scheme for bipartite matchings via a polyhedral viewpoint

2020 ◽  
Author(s):  
Simon Bruggmann ◽  
Rico Zenklusen
Keyword(s):  
Lower Bound ◽  
Submodular Function ◽  
Second Step ◽  
Contention Resolution ◽  
Additional Source ◽  
Submodular Function Maximization ◽  
Versatile Tool ◽  
Resolution Scheme ◽  
Matching Constraints ◽  
Bipartite Case

Abstract Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes round a fractional point by first rounding each coordinate independently, and then dropping some elements to reach a feasible set. Also the second step, where elements are dropped, is typically randomized. This leads to an additional source of randomization within the procedure, which can complicate the analysis. We suggest a different, polyhedral viewpoint to design contention resolution schemes, which avoids to deal explicitly with the randomization in the second step. This is achieved by focusing on the marginals of a dropping procedure. Apart from avoiding one source of randomization, our viewpoint allows for employing polyhedral techniques. Both can significantly simplify the construction and analysis of contention resolution schemes. We show how, through our framework, one can obtain an optimal monotone contention resolution scheme for bipartite matchings, which has a balancedness of 0.4762. So far, only very few results are known about optimality of monotone contention resolution schemes. Our contention resolution scheme for the bipartite case also improves the lower bound on the correlation gap for bipartite matchings. Furthermore, we derive a monotone contention resolution scheme for matchings that significantly improves over the previously best one. More precisely, we obtain a balancedness of 0.4326, improving on a prior 0.1997-balanced scheme. At the same time, our scheme implies that the currently best lower bound on the correlation gap for matchings is not tight. Our results lead to improved approximation factors for various constrained submodular function maximization problems over a combination of matching constraints with further constraints.

scholarly journals Robust monotone submodular function maximization

2018 ◽  
Vol 172 (1-2) ◽  
pp. 505-537 ◽  
Author(s):  
James B. Orlin ◽  
Andreas S. Schulz ◽  
Rajan Udwani
Keyword(s):  
Submodular Function ◽  
Submodular Function Maximization

Approximating Robust Parameterized Submodular Function Maximization in Large-Scales

2019 ◽  
Vol 36 (04) ◽  
pp. 1950022 ◽  
Author(s):  
Ruiqi Yang ◽  
Dachuan Xu ◽  
Yanjun Jiang ◽  
Yishui Wang ◽  
Dongmei Zhang
Keyword(s):  
Submodular Function ◽  
The Other ◽  
Selection Problem ◽  
Cardinality Constraint ◽  
Two Phase ◽  
Submodular Function Maximization ◽  
Set Function ◽  
Submodular Maximization

We study a robust parameterized submodular function maximization inspired by [Mitrović, S, I Bogunovic, A Norouzi-Fard and Jakub Tarnawski (2017). Streaming robust submodular maximization: A partitioned thresholding approach. In Proc. NIPS, pp. 4560–4569] and [Bogunovic, I, J Zhao and V Cevher (2018). Robust maximization of nonsubmodular objectives. In Proc. AISTATS, pp. 890–899]. In our setting, given a parameterized set function, there are two additional twists. One is that elements arrive in a streaming style, and the other is that there are at most [Formula: see text] items deleted from the algorithm’s memory when the stream is finished. The goal is to choose a robust set from the stream such that the robust ratio is maximized. We propose a two-phase algorithm for maximizing a normalized monotone robust parameterized submodular function with a cardinality constraint and show the robust ratio is close to a constant as [Formula: see text]. In the end, we empirically demonstrate the performance of our algorithm on deletion robust support selection problem.

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