Decomposing isotonic regression for efficiently solving large problems

Ronny Luss; Saharon Rosset; Moni Shahar

Decomposing isotonic regression for efficiently solving large problems

Ronny Luss^*, Saharon Rosset, Moni Shahar

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A new algorithm for isotonic regression is presented based on recursively partitioning the solution space. We develop efficient methods for each partitioning subproblem through an equivalent representation as a network flow problem, and prove that this sequence of partitions converges to the global solution. These network flow problems can further be decomposed in order to solve very large problems. Success of isotonic regression in prediction and our algorithm's favorable computational properties are demonstrated through simulated examples as large as 2 × 10 ⁵ variables and 10 ⁷ constraints.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 23
Subtitle of host publication	24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
State	Published - 2010
Event	24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 - Vancouver, BC, Canada Duration: 6 Dec 2010 → 9 Dec 2010

Publication series

Name	Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Conference

Conference	24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
Country/Territory	Canada
City	Vancouver, BC
Period	6/12/10 → 9/12/10

Cite this

Luss, R., Rosset, S., & Shahar, M. (2010). Decomposing isotonic regression for efficiently solving large problems. In Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 (Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010).

Luss, Ronny ; Rosset, Saharon ; Shahar, Moni. / Decomposing isotonic regression for efficiently solving large problems. Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010. 2010. (Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010).

@inproceedings{72a50fc4498e42aeb1825e33087a552e,

title = "Decomposing isotonic regression for efficiently solving large problems",

abstract = "A new algorithm for isotonic regression is presented based on recursively partitioning the solution space. We develop efficient methods for each partitioning subproblem through an equivalent representation as a network flow problem, and prove that this sequence of partitions converges to the global solution. These network flow problems can further be decomposed in order to solve very large problems. Success of isotonic regression in prediction and our algorithm's favorable computational properties are demonstrated through simulated examples as large as 2 × 10 5 variables and 10 7 constraints.",

author = "Ronny Luss and Saharon Rosset and Moni Shahar",

year = "2010",

language = "אנגלית",

isbn = "9781617823800",

series = "Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010",

booktitle = "Advances in Neural Information Processing Systems 23",

note = "null ; Conference date: 06-12-2010 Through 09-12-2010",

}

Luss, R, Rosset, S & Shahar, M 2010, Decomposing isotonic regression for efficiently solving large problems. in Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010. Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010, 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010, Vancouver, BC, Canada, 6/12/10.

Decomposing isotonic regression for efficiently solving large problems. / Luss, Ronny; Rosset, Saharon; Shahar, Moni.

Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010. 2010. (Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Decomposing isotonic regression for efficiently solving large problems

AU - Luss, Ronny

AU - Rosset, Saharon

AU - Shahar, Moni

PY - 2010

Y1 - 2010

N2 - A new algorithm for isotonic regression is presented based on recursively partitioning the solution space. We develop efficient methods for each partitioning subproblem through an equivalent representation as a network flow problem, and prove that this sequence of partitions converges to the global solution. These network flow problems can further be decomposed in order to solve very large problems. Success of isotonic regression in prediction and our algorithm's favorable computational properties are demonstrated through simulated examples as large as 2 × 10 5 variables and 10 7 constraints.

AB - A new algorithm for isotonic regression is presented based on recursively partitioning the solution space. We develop efficient methods for each partitioning subproblem through an equivalent representation as a network flow problem, and prove that this sequence of partitions converges to the global solution. These network flow problems can further be decomposed in order to solve very large problems. Success of isotonic regression in prediction and our algorithm's favorable computational properties are demonstrated through simulated examples as large as 2 × 10 5 variables and 10 7 constraints.

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M3 - פרסום בספר כנס

AN - SCOPUS:84860644999

SN - 9781617823800

T3 - Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

BT - Advances in Neural Information Processing Systems 23

Y2 - 6 December 2010 through 9 December 2010

ER -

Luss R, Rosset S, Shahar M. Decomposing isotonic regression for efficiently solving large problems. In Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010. 2010. (Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010).

Decomposing isotonic regression for efficiently solving large problems

Abstract

Publication series

Conference

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