research-article

Actively learning level-sets of composite functions

Authors:

Jeff SchneiderAuthors Info & Claims

ICML '08: Proceedings of the 25th international conference on Machine learning

Pages 80 - 87

https://doi.org/10.1145/1390156.1390167

Published: 05 July 2008 Publication History

Abstract

Scientists frequently have multiple types of experiments and data sets on which they can test the validity of their parameterized models and locate plausible regions for the model parameters. By examining multiple data sets, scientists can obtain inferences which typically are much more informative than the deductions derived from each of the data sources independently. Several standard data combination techniques result in target functions which are a weighted sum of the observed data sources. Thus, computing constraints on the plausible regions of the model parameter space can be formulated as finding a level set of a target function which is the sum of observable functions. We propose an active learning algorithm for this problem which selects both a sample (from the parameter space) and an observable function upon which to compute the next sample. Empirical tests on synthetic functions and on real data for an eight parameter cosmological model show that our algorithm significantly reduces the number of samples required to identify the desired level-set.

References

[1]

Angluin, D. (1988). Queries and concept learning. Machine Learning, 2, 319--342.

[2]

Bennett, C. L., et al. (2003). First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission. Astrophysical Journal Supplemental, 148, 97--117.

[3]

Bryan, B. (2007). Actively learning specific function properties with application to statistical inference. Doctoral dissertation, Carnegie Mellon University.

Digital Library

[4]

Bryan, B., et al. (2005). Active learning for identifying function threshold boundaries. In Advances in neural information processing systems 18. Cambridge, MA: MIT Press.

[5]

Cressie, N. (1991). Statistics for spatial data. New York: Wiley.

[6]

Davis, T. M., et al. (2007). Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes. Astrophysical Journal, 666, 716.

[7]

Fisher, R. (1932). Statistical methods for research workers. London: Oliver and Boyd. 4 edition.

[8]

Guestrin, C., et al. (2005). Near-optimal sensor placements in gaussian processes. ICML 2005: Proceedings of the 22nd International Conference on Machine learning. ACM Press.

Digital Library

[9]

Hedges, L. V. (1985). Statistical methods for meta-analysis. Academic Press.

[10]

Kersting, K. et al. (2007). Most likely heteroscedastic gaussian process regression. ICML '07: Proceedings of the 24th International Conference on Machine Learning. ACM Press.

Digital Library

[11]

MacKay, D. (1992). Information-based objective functions for active data selection. Neural Computation, 4, 590.

Digital Library

[12]

Ramakrishnan, N., et al. (2005). Gaussian processes for active data mining of spatial aggregates. Proceedings of the SIAM International Conference on Data Mining.

[13]

Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.

Digital Library

[14]

Santner, T. J., Williams, B. J., & Notz, W. (2003). The design and analyis of computer experiments. Springer. 1 edition.

[15]

Shmueli, G., & Fienberg, S. E. (2006). Statistical methods in counterterrorism, chapter Current and Potential Statistical Methods for Monitoring Multiple Data Streams for Biosurveillance, 109. New York: Springer.

[16]

Spergel, D. et al. (2003). First-Year Wilkinson Microwave Anisotropy Probe Observations: Determination of Cosmological Parameters. Astrophysical Journal Supplemental, 148.

[17]

Tegmark, M., et al. (2006). Cosmological constraints from the SDSS luminous red galaxies. Physical Review D, 74, 123507.

Cited By

Cole DGramacy RWarner JBomarito GLeser PLeser W(2022)Entropy-based adaptive design for contour finding and estimating reliabilityJournal of Quality Technology10.1080/00224065.2022.205379555:1(43-60)Online publication date: 8-Apr-2022
https://doi.org/10.1080/00224065.2022.2053795
Lyu XBinois MLudkovski M(2021)Evaluating Gaussian process metamodels and sequential designs for noisy level set estimationStatistics and Computing10.1007/s11222-021-10014-w31:4Online publication date: 26-May-2021
https://doi.org/10.1007/s11222-021-10014-w
Suryan VTokekar P(2020)Learning a Spatial Field in Minimum Time With a Team of RobotsIEEE Transactions on Robotics10.1109/TRO.2020.299400336:5(1562-1576)Online publication date: Oct-2020
https://doi.org/10.1109/TRO.2020.2994003
Show More Cited By

Index Terms

Actively learning level-sets of composite functions
1. Computing methodologies
  1. Machine learning
  2. Modeling and simulation
    1. Model development and analysis
      1. Model verification and validation
      2. Modeling methodologies
2. Theory of computation
  1. Theory and algorithms for application domains
    1. Machine learning theory
      1. Inductive inference

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Published In

cover image ACM Other conferences

ICML '08: Proceedings of the 25th international conference on Machine learning

July 2008

1310 pages

ISBN:9781605582054

DOI:10.1145/1390156

General Chair:
William Cohen
Carnegie Mellon University
,
Program Chairs:
Andrew McCallum
University of Massachusetts Amherst
,
Sam Roweis
University of Toronto and Google

Copyright © 2008 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Pascal
University of Helsinki
Xerox
Federation of Finnish Learned Societies
Google Inc.
NSF
Machine Learning Journal/Springer
Microsoft Research: Microsoft Research
Intel: Intel
Yahoo!
Helsinki Institute for Information Technology
IBM: IBM

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 July 2008

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ICML '08

Sponsor:

Microsoft Research
Intel
IBM

ICML '08: The 25th Annual International Conference on Machine Learning held in conjunction with the 2007 International Conference on Inductive Logic Programming

July 5 - 9, 2008

Helsinki, Finland

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Overall Acceptance Rate 140 of 548 submissions, 26%

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Cited By

Cole DGramacy RWarner JBomarito GLeser PLeser W(2022)Entropy-based adaptive design for contour finding and estimating reliabilityJournal of Quality Technology10.1080/00224065.2022.205379555:1(43-60)Online publication date: 8-Apr-2022
https://doi.org/10.1080/00224065.2022.2053795
Lyu XBinois MLudkovski M(2021)Evaluating Gaussian process metamodels and sequential designs for noisy level set estimationStatistics and Computing10.1007/s11222-021-10014-w31:4Online publication date: 26-May-2021
https://doi.org/10.1007/s11222-021-10014-w
Suryan VTokekar P(2020)Learning a Spatial Field in Minimum Time With a Team of RobotsIEEE Transactions on Robotics10.1109/TRO.2020.299400336:5(1562-1576)Online publication date: Oct-2020
https://doi.org/10.1109/TRO.2020.2994003
Bogunovic IScarlett JKrause ACevher V(2016)Truncated variance reductionProceedings of the 30th International Conference on Neural Information Processing Systems10.5555/3157096.3157266(1515-1523)Online publication date: 5-Dec-2016
https://dl.acm.org/doi/10.5555/3157096.3157266
Huttunen JStark P(2012)Cheap contouring of costly functions: the Pilot Approximation Trajectory algorithmComputational Science & Discovery10.1088/1749-4699/5/1/0150065:1(015006)Online publication date: 30-Aug-2012
https://doi.org/10.1088/1749-4699/5/1/015006
Valada ATomaszewski CKannan BVelagapudi PKantor GScerri P(2012)An intelligent approach to hysteresis compensation while sampling using a fleet of autonomous watercraftProceedings of the 5th international conference on Intelligent Robotics and Applications - Volume Part II10.1007/978-3-642-33515-0_47(472-485)Online publication date: 3-Oct-2012
https://dl.acm.org/doi/10.1007/978-3-642-33515-0_47

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