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Approximate Location of Relevant Variables under the Crossover Distribution

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Stochastic Algorithms: Foundations and Applications (SAGA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2264))

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Abstract

Searching for genes involved in traits (e.g. diseases), based on genetic data, is considered from a computational learning perspective. This leads to the problem of learning relevant variables of functions from data sampled from a certain class of distributions generalizing the uniform distribution. The Fourier transform of Boolean functions is applied to translate the problem into searching for local extrema of certain functions of observables. We work out the combinatorial structure of this approach and illustrate its potential use.

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References

  1. D.A. Bell, H. Wang: A formalism for relevance and its application in feature subset selection, Machine Learning 41 (2000), 175–195

    Article  MATH  Google Scholar 

  2. A. Bernasconi: Mathematical techniques for the analysis of Boolean functions, PhD thesis, Univ. Pisa 1998

    Google Scholar 

  3. N. Bshouty, J.C. Jackson, C. Tamon: More efficient PAC-learning of DNF with membership queries under the uniform distribution, ACM Symp. on Computational Learning Theory COLT’99, 286–293

    Google Scholar 

  4. P. Damaschke: Adaptive versus nonadaptive attribute-efficient learning, Machine Learning 41 (2000), 197–215

    Article  MATH  Google Scholar 

  5. P. Damaschke: Parallel attribute-efficient learning of monotone Boolean functions, 7th Scand. Workshop on Algorithm Theory SWAT’2000, LNCS 1851, 504–512, journal version accepted for J. of Computer and System Sciences

    Google Scholar 

  6. A.S. Goldstein, E.M. Reingold: A Fibonacci version of Kraft’s inequality with an application to discrete unimodal search, SIAM J. Computing 22 (1993), 751–777

    Article  MATH  MathSciNet  Google Scholar 

  7. J.C. Jackson: An efficient membership-query algorithm for learning DNF with respect to the uniform distribution, J. of Comp. and Sys. Sci. 55 (1997), 414–440

    Article  MATH  Google Scholar 

  8. G.H. John, R. Kohavi, K. Pfleger: Irrelevant features and the subset selection problem, 11th Int. Conf. on Machine Learning 1994, Morgan Kaufmann, 121–129

    Google Scholar 

  9. D.S. Johnson (ed.): Challenges for Theoretical Computer Science (draft), available at http://www.research.att.com/~dsj/nflist.html#Biology

  10. S. Karlin, U. Liberman: Classifications and comparisons of multilocus recombination distribution, Proc. Nat. Acad. Sci. USA 75 (1979), 6332–6336

    Google Scholar 

  11. M.J. Kearns, R.E. Schapire: Efficient distribution-free learning of probabilistic concepts, in: Computational Learning Theory and Natural Learning Systems, MIT Press 1994, 289–329 (preliminary version in FOCS’90)

    Google Scholar 

  12. R. Kohavi: Feature subset selection as search with probabilistic estimates, in: R. Greiner, D. Subramanian (eds.): Relevance, Proc. 1994 AAAI Fall Symposium, 122–126

    Google Scholar 

  13. W. Li, J. Reich: A complete enumeration and classification of two-locus disease models, Human Hereditary (1999)

    Google Scholar 

  14. N. Linial, Y. Mansour, N. Nisan: Constant depth circuits, Fourier transform, and learnability, J. of ACM 40 (1993), 607–620

    Article  MATH  MathSciNet  Google Scholar 

  15. Y. Mansour: Learning Boolean functions via the Fourier transform, in: Theoretical Advances in Neural Computing and Learning, Kluwer 1994

    Google Scholar 

  16. A. Mathur, E.M. Reingold: Generalized Kraft’s inequality and discrete k-modal search, SIAM J. Computing 25 (1996), 420–447

    Article  MATH  MathSciNet  Google Scholar 

  17. J.C. Schlimmer: Efficiently inducing determinations: a complete and systematic search algorithm that uses optimal pruning, 10th Int. Conf. on Machine Learning 1993, Morgan Kaufmann, 284–290

    Google Scholar 

  18. J.D. Terwilliger, H.H.H. Göring: Gene mapping in the 20th and 21st centuries: statistical methods, data analysis, and experimental design, Human Biology 72 (2000), 63–132

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematical and Computing Sciences, Chalmers University, 41296, Göteborg, Sweden

    Peter Damaschke

Authors
  1. Peter Damaschke
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Editor information

Editors and Affiliations

  1. Institute for Computer Architecture and Software Engineering, GMD - National ResearchCenter for Information Technology, Kekuléstr.7, 12489, Berlin-Adlershof, Germany

    Kathleen Steinhöfel

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© 2001 Springer-Verlag Berlin Heidelberg

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Damaschke, P. (2001). Approximate Location of Relevant Variables under the Crossover Distribution. In: Steinhöfel, K. (eds) Stochastic Algorithms: Foundations and Applications. SAGA 2001. Lecture Notes in Computer Science, vol 2264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45322-9_13

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  • DOI: https://doi.org/10.1007/3-540-45322-9_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43025-4

  • Online ISBN: 978-3-540-45322-2

  • eBook Packages: Springer Book Archive

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