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2015 | 5 | 525--535
Tytuł artykułu

Small Populations, High-Dimensional Spaces: Sparse Covariance Matrix Adaptation

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Evolution strategies are powerful evolutionary algorithms for continuous optimization. The main search operator is mutation. Its extend is controlled by the covariance matrix and must be adapted during a run. Modern Evolution Strategies accomplish this with covariance matrix adaptation techniques. However, the quality of the common estimate of the covariance is known to be questionable for high search space dimensions. This paper introduces a new approach by changing the coordinate system and introducing sparse covariance matrix techniques. The results are evaluated in experiments. (original abstract)
Słowa kluczowe
PL
EN
Rocznik
Tom
5
Strony
525--535
Opis fizyczny
Twórcy
  • Universitat der Bundeswehr Munchen, Germany
autor
  • Universitat der Bundeswehr Munchen, Germany
Bibliografia
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  • A. E. Eiben and J. E. Smith, Introduction to Evolutionary Computing, ser. Natural Computing Series. Berlin: Springer, 2003.
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  • H.-G. Beyer and H.-P. Schwefel, "Evolution strategies: A comprehensive introduction," Natural Computing, vol. 1, no. 1, pp. 3-52, 2002.
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  • H.-G. Beyer and S. Meyer-Nieberg, "Self-adaptation of evolution strategies under noisy fitness evaluations," Genetic Programming and Evolvable Machines, vol. 7, no. 4, pp. 295-328, 2006.
  • N. Hansen, "The CMA evolution strategy: A comparing review," in Towards a new evolutionary computation. Advances in estimation of distribution algorithms, J. Lozano et al., Eds. Springer, 2006, pp. 75- 102.
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  • "Estimation of a covariance matrix," in Rietz Lecture, 39th Annual Meeting. Atlanta, GA: IMS, 1975.
  • J. Schaffer and K. Strimmer, "A shrinkage approach to large-scale ¨ covariance matrix estimation and implications for functional genomics,," Statistical Applications in Genetics and Molecular Biology, vol. 4, no. 1, p. Article 32, 2005.
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  • E. Levina, A. Rothman, and J. Zhu, "Sparse estimation of large covariance matrices via a nested lasso penalty," Ann. Appl. Stat., vol. 2, no. 1, pp. 245-263, 03 2008. doi: 10.1214/07-AOAS139. [Online]. Available: http://dx.doi.org/10.1214/07-AOAS139
  • ] T. J. Fisher and X. Sun, "Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrix," Computational Statistics & Data Analysis, vol. 55, no. 5, pp. 1909 - 1918, 2011. doi: http://dx.doi.org/10.1016/j.csda.2010.12.006. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0167947310004743
  • X. Chen, Z. Wang, and M. McKeown, "Shrinkage-to-tapering estimation of large covariance matrices," Signal Processing, IEEE Transactions on, vol. 60, no. 11, pp. 5640-5656, 2012. doi: 10.1109/TSP.2012.2210546
  • T. Cai and W. Liu, "Adaptive thresholding for sparse covariance matrix estimation," Journal of the American Statistical Association, vol. 106, no. 494, pp. 672-684, 2011.
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  • N. Hansen, "Adaptive encoding: How to render search coordinate system invariant," in Parallel Problem Solving from Nature - PPSN X, ser. Lecture Notes in Computer Science, G. Rudolph, T. Jansen, N. Beume, S. Lucas, and C. Poloni, Eds. Springer Berlin Heidelberg, 2008, vol. 5199, pp. 205-214. ISBN 978-3-540-87699-1. [Online]. Available: http://dx.doi.org/10.1007/978-3-540-87700-4 21
  • M. Pourahmadi, High-Dimensional Covariance Estimation: With HighDimensional Data. John Wiley & Sons, 2013.
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  • S. Finck, N. Hansen, R. Ros, and A. Auger, "Real-parameter black-box optimization benchmarking 2010: Presentation of the noiseless functions," Institute National de Recherche en Informatique et Automatique, Tech. Rep., 2010, 2009/22.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171422528

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