A new philosophy for model selection and performance estimation of data- based approximate mappings

M. R. Banan, Keith Hjelmstad

Research output: Contribution to journalArticle

Abstract

The MC-HARP algorithm uses a Monte Carlo strategy in conjunction with a hierarchical adaptive random partitioning scheme to develop data-based approximate mappings. An estimate of the variance of the Monte Carlo sample for every point in the domain (as opposed to only data points) is a natural artifact of the MC-HARP algorithm. We define global measures, computed from the approximation variance function, that are indicative of the performance of the approximation. We show how these performance indices can be used to select an MC-HARP model with optimal complexity when the data are polluted with noise. The proposed approach represents a philosophical departure from currently available sampling-based techniques for model selection and performance estimation and has distinct advantages when spatial relationships among the data are important.

Original languageEnglish (US)
Pages (from-to)13-29
Number of pages17
JournalMathematical and Computer Modelling
Volume24
Issue number1
DOIs
StatePublished - Jul 1996
Externally publishedYes

Fingerprint

Model Selection
Sampling
Variance Function
Approximation
Performance Index
Partitioning
Distinct
Philosophy
Model selection
Estimate
Performance index
Model

Keywords

  • Adaptive partitioning
  • Approximation
  • Data-fitting
  • Model selection
  • Monte Carlo
  • Neural networks

ASJC Scopus subject areas

  • Information Systems and Management
  • Control and Systems Engineering
  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

A new philosophy for model selection and performance estimation of data- based approximate mappings. / Banan, M. R.; Hjelmstad, Keith.

In: Mathematical and Computer Modelling, Vol. 24, No. 1, 07.1996, p. 13-29.

Research output: Contribution to journalArticle

@article{22ebd1791f89473d8288961e6431d77d,
title = "A new philosophy for model selection and performance estimation of data- based approximate mappings",
abstract = "The MC-HARP algorithm uses a Monte Carlo strategy in conjunction with a hierarchical adaptive random partitioning scheme to develop data-based approximate mappings. An estimate of the variance of the Monte Carlo sample for every point in the domain (as opposed to only data points) is a natural artifact of the MC-HARP algorithm. We define global measures, computed from the approximation variance function, that are indicative of the performance of the approximation. We show how these performance indices can be used to select an MC-HARP model with optimal complexity when the data are polluted with noise. The proposed approach represents a philosophical departure from currently available sampling-based techniques for model selection and performance estimation and has distinct advantages when spatial relationships among the data are important.",
keywords = "Adaptive partitioning, Approximation, Data-fitting, Model selection, Monte Carlo, Neural networks",
author = "Banan, {M. R.} and Keith Hjelmstad",
year = "1996",
month = "7",
doi = "10.1016/0895-7177(96)00077-5",
language = "English (US)",
volume = "24",
pages = "13--29",
journal = "Mathematical and Computer Modelling",
issn = "0895-7177",
publisher = "Elsevier Limited",
number = "1",

}

TY - JOUR

T1 - A new philosophy for model selection and performance estimation of data- based approximate mappings

AU - Banan, M. R.

AU - Hjelmstad, Keith

PY - 1996/7

Y1 - 1996/7

N2 - The MC-HARP algorithm uses a Monte Carlo strategy in conjunction with a hierarchical adaptive random partitioning scheme to develop data-based approximate mappings. An estimate of the variance of the Monte Carlo sample for every point in the domain (as opposed to only data points) is a natural artifact of the MC-HARP algorithm. We define global measures, computed from the approximation variance function, that are indicative of the performance of the approximation. We show how these performance indices can be used to select an MC-HARP model with optimal complexity when the data are polluted with noise. The proposed approach represents a philosophical departure from currently available sampling-based techniques for model selection and performance estimation and has distinct advantages when spatial relationships among the data are important.

AB - The MC-HARP algorithm uses a Monte Carlo strategy in conjunction with a hierarchical adaptive random partitioning scheme to develop data-based approximate mappings. An estimate of the variance of the Monte Carlo sample for every point in the domain (as opposed to only data points) is a natural artifact of the MC-HARP algorithm. We define global measures, computed from the approximation variance function, that are indicative of the performance of the approximation. We show how these performance indices can be used to select an MC-HARP model with optimal complexity when the data are polluted with noise. The proposed approach represents a philosophical departure from currently available sampling-based techniques for model selection and performance estimation and has distinct advantages when spatial relationships among the data are important.

KW - Adaptive partitioning

KW - Approximation

KW - Data-fitting

KW - Model selection

KW - Monte Carlo

KW - Neural networks

UR - http://www.scopus.com/inward/record.url?scp=0030186857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030186857&partnerID=8YFLogxK

U2 - 10.1016/0895-7177(96)00077-5

DO - 10.1016/0895-7177(96)00077-5

M3 - Article

VL - 24

SP - 13

EP - 29

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 1

ER -