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Computing the Maximum Bichromatic Discrepancy, with Applications to Computer Graphics and Machine Learning

David P. Dobkin, Dimitrios Gunopulos, Wolfgang Maass
1996 Journal of computer and system sciences (Print)  
Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics.  ...  In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, including rectangles and halfspaces.  ...  ACKNOWLEDGMENT The authors would-like to thank Bernard Chazelle and David Haussler for helpful communications regarding the research for this papery and two anonymous referees for their suggestions.  ... 
doi:10.1006/jcss.1996.0034 fatcat:gw43mtlgh5b73mxtqo4lbsywze

Page 1169 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
bichromatic discrepancy, with applications to computer graphics and machine learning.  ...  It is shown that the minimizing disagreement problem and the computation of the maximum bichromatic dis- crepancy are equivalent. Extensions to other discrepancy problems are also given.  ... 

Page 1904 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
Dobkin, Dimitrios Gunop- ulos and Wolfgang Maass, Computing the maximum bichromatic discrepancy, with applications to computer graphics and machine learning (453—470); Michael Frazier, Sally Goldman, Nina  ...  computers with fixed and reconfigurable buses: packet routing and sorting.  ... 

The hunting of the bump

Deepak Agarwal, Jeff M. Phillips, Suresh Venkatasubramanian
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
We present an algorithm running in O( 1 ǫ n 2 log 2 n) that computes the maximum discrepancy rectangle to within additive error ǫ, for the Kulldorff scan statistic.  ...  An anomalous region is thus defined to be one with high discrepancy. In this paper, we present algorithms for maximizing statistical discrepancy functions over the space of axis-parallel rectangles.  ...  Subsequently Dobkin, Gunopulous, and Maass [5] developed algorithms for computing maximum bichromatic discrepancy over axis-parallel rectangular regions, where the bichromatic discrepancy of a region  ... 
doi:10.1145/1109557.1109683 fatcat:3unb7kuovvftvgsu6mhe2swkxq

The Hunting of the Bump: On Maximizing Statistical Discrepancy [article]

Deepak Agarwal and Jeff M. Phillips and Suresh Venkatasubramanian
2005 arXiv   pre-print
We present an algorithm running in O([tb]1/ϵ n^2 ^2 n) that computes the maximum discrepancy rectangle to within additive error ϵ, for the Kulldorff scan statistic.  ...  An anomalous region is thus defined to be one with high discrepancy. In this paper, we present algorithms for maximizing statistical discrepancy functions over the space of axis-parallel rectangles.  ...  Subsequently Dobkin, Gunopulous, and Maass [5] developed algorithms for computing maximum bichromatic discrepancy over axis-parallel rectangular regions, where the bichromatic discrepancy of a region  ... 
arXiv:cs/0510004v1 fatcat:vm6eqbea5fgrbepsj2q4cposfi

Approximate Maximum Halfspace Discrepancy [article]

Michael Matheny, Jeff M. Phillips
2021 arXiv   pre-print
In this context the maximum discrepancy problem is to find the h^* = max_h ∈ (X, ℋ_d)Φ(h). We aim to instead find an ĥ such that Φ(h^*) - Φ(ĥ) ≤ε.  ...  This is the central problem in linear classification for machine learning, in spatial scan statistics for spatial anomaly detection, and shows up in many other areas.  ...  Computing the discrepancy with applications to supersampling patterns. ACM Transactions on Graphics, 15:354–376, 1996. 18 Anka Gajentaan and Mark H. Overmars.  ... 
arXiv:2106.13851v1 fatcat:5ea37wfwpfe7lnsmyzakcssryy

Computing optimal islands

C. Bautista-Santiago, J.M. Díaz-Báñez, D. Lara, P. Pérez-Lantero, J. Urrutia, I. Ventura
2011 Operations Research Letters  
Our approach also optimizes other parameters and gives an approximation to the class cover problem.  ...  In this paper we give an O(n 3 )-time algorithm to find a monochromatic island of maximum cardinality.  ...  Acknowledgements Authors Díaz-Báñez, Pérez-Lantero, Urrutia and Ventura were supported by Spanish MEC grants MTM2006-03909 and MTM2009-08625.  ... 
doi:10.1016/j.orl.2011.04.008 fatcat:k6jjcmcp3jeibawnfjoud5qwla

On the coarseness of bicolored point sets

S. Bereg, J.M. Díaz-Báñez, D. Lara, P. Pérez-Lantero, C. Seara, J. Urrutia
2013 Computational geometry  
The coarseness of S is the discrepancy of the convex partition of S with maximum discrepancy. We study the coarseness of bicolored point sets, and relate it to well blended point sets.  ...  For X ⊆ S, let ∇(X) = ||X ∩ R| − |X ∩ B|| be the bichromatic discrepancy of X.  ...  Finally, we make reference to papers that consider the computation of geometric objects with maximum discrepancy and their applications to computer graphics and machine learning.  ... 
doi:10.1016/j.comgeo.2012.04.003 fatcat:bbkbuoiynja4patazn4ujiv5pu

Geometric Optimization Revisited [chapter]

Pankaj K. Agarwal, Esther Ezra, Kyle Fox
2019 Lecture Notes in Computer Science  
We review the progress made in recent years on a number of such geometric optimization problems, with an emphasis on how geometry has been exploited to develop better algorithms.  ...  Instead of discussing many problems, we focus on a few problems, namely, set cover, hitting set, independent set, and computing maps between point sets.  ...  We thank Timothy Chan, Sariel Har-Peled, and Micha Sharir for their helpful comments.  ... 
doi:10.1007/978-3-319-91908-9_5 fatcat:3l3jwv5bevhkvoyi3gtb65g7ae

Bichromatic separability with two boxes: A general approach

C. Cortés, J.M. Díaz-Báñez, P. Pérez-Lantero, C. Seara, J. Urrutia, I. Ventura
2009 Journal of Algorithms  
We introduce the first known data structure to dynamically maintain the optimal solution of this problem.  ...  We prove that this problem can be solved in O(n 2 log n) time and O(n) space. Our approach is based on solving some instances of Bentley's maximum-sum consecutive subsequence problem.  ...  We also show a generalization of our approach that can be used to solve a general type of problem of interest in areas such as computer graphics or machine learning [7] .  ... 
doi:10.1016/j.jalgor.2009.01.001 fatcat:zsckxoxi65e2xmzcz5l6rizdta

Software tools for quantum control: Improving quantum computer performance through noise and error suppression [article]

Harrison Ball, Michael J. Biercuk, Andre Carvalho, Jiayin Chen, Michael Hush, Leonardo A. De Castro, Li Li, Per J. Liebermann, and Harry J. Slatyer, Claire Edmunds, Virginia Frey, Cornelius Hempel (+1 others)
2020 arXiv   pre-print
In this manuscript we introduce software tools for the application and integration of quantum control in quantum computing research, serving the needs of hardware R&D teams, algorithm developers, and end  ...  Fortunately quantum control enables efficient execution of quantum logic operations and algorithms with built-in robustness to errors, without the need for complex logical encoding.  ...  BLACK OPAL helps users learn about quantum computing and quantum control in the NISQ era by taking advantage of a graphical interface with interactive visualizations.  ... 
arXiv:2001.04060v2 fatcat:7x5olheg3bfovhqcosyyuicgpi

Identifying, attributing and describing spatial bursts

Michael Mathioudakis, Nilesh Bansal, Nick Koudas
2010 Proceedings of the VLDB Endowment  
At the heart of our proposal lie efficient algorithms that identify geographically focused information bursts, attribute them to demographic factors and identify sets of descriptive keywords.  ...  We demonstrate the scalability and practical utility of our proposal running on top of a multi-terabyte text collection.  ...  We submitted the query 'cricket' to BlogScope with a temporal restriction on the first 10 days of March 2008.  ... 
doi:10.14778/1920841.1920978 fatcat:qlq3uekjzfbs5mh4ye7dllf5cm

Page 1606 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(with Gunopulos, Dimitris; Maass, Wolfgang) Computing the maximum bichromatic discrepancy, with applications to computer graphics and machine learning.  ...  An efficient membership-query alogithm for learning DNF with respect to the uniform distribution. (English summary) COMPUTER SCIENCE 1998 1606 Jain, Sanjay' (with Sharma, Arun K.)  ... 

Page 1014 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(Summary) 98f:42029 42C15 (41A15) Maass, Wolfgang (with Dobkin, David P.; Gunopulos, Dimitris) Computing the maximum bichromatic discrepancy, with applications to computer graphics and machine learning  ...  (Rani Siromoney) 98b:68159 68T0S (68U05) — Bounds for the computational power and learning complexity of analog neural nets. (English summary) S/AM J. Comput. 26 (1997), no. 3, 708-732.  ... 

Free‐field reciprocity calibration of laboratory standard (LS) microphones using a time selective technique

Knud Rasmussen, Salvador Barrera‐Figueroa
2006 Journal of the Acoustical Society of America  
To handle segments with a large number of dimensions, a support vector machine ͑SVM͒ is used.  ...  computers, and conventional methods can be applicable to relatively small ͑up to order of 10 000 boundary elements͒ problems.  ...  From both statistical graphical modeling and regression tree analysis, the speaking rate, F0 declination, and spectral tilt were found to be dominant acoustic correlates to the perceived age.  ... 
doi:10.1121/1.4788231 fatcat:o5zthkauwvddtjcer4wralkeja
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