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Computing the Maximum Bichromatic Discrepancy, with Applications to Computer Graphics and Machine Learning
1996
Journal of computer and system sciences (Print)
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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
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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
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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
2006
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
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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]
2005
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
2011
Operations Research Letters
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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
2013
Computational geometry
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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]
2019
Lecture Notes in Computer Science
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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
2009
Journal of Algorithms
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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]
2020
arXiv
pre-print
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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
2010
Proceedings of the VLDB Endowment
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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
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(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
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(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
2006
Journal of the Acoustical Society of America
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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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