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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)
*

*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. ...

##
###
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

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

doi:10.1145/1109557.1109683
fatcat:3unb7kuovvftvgsu6mhe2swkxq
*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 ...##
###
The Hunting of the Bump: On Maximizing Statistical Discrepancy
[article]

2005
*
arXiv
*
pre-print

We present an algorithm running in O([tb]1/ϵ n^2 ^2 n) that

arXiv:cs/0510004v1
fatcat:vm6eqbea5fgrbepsj2q4cposfi
*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 ...##
###
Approximate Maximum Halfspace Discrepancy
[article]

2021
*
arXiv
*
pre-print

In this context

arXiv:2106.13851v1
fatcat:5ea37wfwpfe7lnsmyzakcssryy
*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. ...##
###
Computing optimal islands

2011
*
Operations Research Letters
*

Our approach also optimizes other parameters

doi:10.1016/j.orl.2011.04.008
fatcat:k6jjcmcp3jeibawnfjoud5qwla
*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. ...##
###
On the coarseness of bicolored point sets

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*. ...

##
###
Geometric Optimization Revisited
[chapter]

2019
*
Lecture Notes in Computer Science
*

We review

doi:10.1007/978-3-319-91908-9_5
fatcat:3l3jwv5bevhkvoyi3gtb65g7ae
*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. ...##
###
Bichromatic separability with two boxes: A general approach

2009
*
Journal of Algorithms
*

We introduce

doi:10.1016/j.jalgor.2009.01.001
fatcat:zsckxoxi65e2xmzcz5l6rizdta
*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] . ...##
###
Software tools for quantum control: Improving quantum computer performance through noise and error suppression
[article]

2020
*
arXiv
*
pre-print

In this manuscript we introduce software tools for

arXiv:2001.04060v2
fatcat:7x5olheg3bfovhqcosyyuicgpi
*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. ...##
###
Identifying, attributing and describing spatial bursts

2010
*
Proceedings of the VLDB Endowment
*

At

doi:10.14778/1920841.1920978
fatcat:qlq3uekjzfbs5mh4ye7dllf5cm
*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. ...##
###
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

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. ...

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