Linear time isotonic and unimodal regression in the L 1 and L ∞ norms
We consider L 1 -isotonic regression and L ∞ isotonic and unimodal regression. For L 1 -isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is boun...
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| Vydáno v: | Journal of discrete algorithms (Amsterdam, Netherlands) Ročník 4; číslo 4; s. 676 - 691 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.12.2006
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| Témata: | |
| ISSN: | 1570-8667, 1570-8675 |
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| Abstract | We consider
L
1
-isotonic regression and
L
∞
isotonic and unimodal regression. For
L
1
-isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for
L
∞
isotonic and unimodal regression. |
|---|---|
| AbstractList | We consider
L
1
-isotonic regression and
L
∞
isotonic and unimodal regression. For
L
1
-isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for
L
∞
isotonic and unimodal regression. |
| Author | Boyarshinov, Victor Magdon-Ismail, Malik |
| Author_xml | – sequence: 1 givenname: Victor surname: Boyarshinov fullname: Boyarshinov, Victor email: boyarv@cs.rpi.edu – sequence: 2 givenname: Malik surname: Magdon-Ismail fullname: Magdon-Ismail, Malik email: magdon@cs.rpi.edu |
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| CitedBy_id | crossref_primary_10_1214_18_AOS1792 crossref_primary_10_1007_s11228_010_0150_z crossref_primary_10_1016_j_camwa_2009_04_003 crossref_primary_10_1198_106186008X285591 crossref_primary_10_1016_j_jcss_2009_04_005 crossref_primary_10_1109_TSP_2009_2028937 |
| Cites_doi | 10.1016/0021-9045(74)90044-6 10.1214/aoms/1177698335 10.1007/PL00009258 10.1214/aoms/1177728423 10.1287/moor.14.2.303 10.1016/0021-9045(74)90075-6 10.2307/2347399 10.1016/0893-9659(95)00013-G 10.1007/3-540-45675-9_61 10.2307/2532850 |
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| Keywords | Output sensitive algorithm Median Approximation Monotonic Shape constrained |
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| References_xml | – reference: R.A. Mureika, T.R. Turner, P.C. Wollan, An algorithm for unimodal isotonic regression with application to locating a maximum, Technical Report 92-4, Department of Mathematics and Statistics, University of New Brunswick, 1992 – volume: vol. 9 start-page: 634 year: 1997 end-page: 640 ident: bib014 article-title: Monotonicity hints publication-title: Advances in Neural Information Processing Systems (NIPS) – year: 1955 ident: bib001 article-title: An empirical distribution function for sampling with incomplete information publication-title: Ann. Math. Statist. – volume: 39 start-page: 397 year: 1990 end-page: 424 ident: bib006 article-title: Isotonic regression for umbrella orderings publication-title: Appl. Statist. – volume: 8 start-page: 67 year: 1995 end-page: 70 ident: bib011 article-title: Efficient computation of an isotonic median regression publication-title: Appl. Math. 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Lett. doi: 10.1016/0893-9659(95)00013-G – year: 1971 ident: 10.1016/j.jda.2005.07.001_bib002 article-title: Isotonic approximation – year: 2001 ident: 10.1016/j.jda.2005.07.001_bib004 – ident: 10.1016/j.jda.2005.07.001_bib007 doi: 10.1007/3-540-45675-9_61 – volume: 52 start-page: 1363 year: 1996 ident: 10.1016/j.jda.2005.07.001_bib009 article-title: Subset selection with additional order information publication-title: Biometrics doi: 10.2307/2532850 – volume: 32 year: 2000 ident: 10.1016/j.jda.2005.07.001_bib015 article-title: Optimal algorithms for unimodal regression publication-title: Comput. Sci. Statist. – volume: 35 start-page: 304 year: 1980 ident: 10.1016/j.jda.2005.07.001_bib005 article-title: Unimodal regression publication-title: The Statistician |
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| Snippet | We consider
L
1
-isotonic regression and
L
∞
isotonic and unimodal regression. For
L
1
-isotonic regression, we present a linear time algorithm when the number... |
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| Title | Linear time isotonic and unimodal regression in the L 1 and L ∞ norms |
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