Advertisement

Testing Juntas: A Brief Survey

  • Eric Blais
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6390)

Abstract

A function on n variables is called a k-junta if it depends on at most k of its variables. In this survey, we review three recent algorithms for testing k-juntas with few queries.

Keywords

Boolean Function Binary Search Query Complexity Property Testing Testing Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atıcı, A., Servedio, R.A.: Quantum algorithms for learning and testing juntas. Quantum Information Processing 6(5), 323–348 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bounds by polynomials. J. of the ACM 48(4), 778–797 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bellare, M., Coppersmith, D., Håstad, J., Kiwi, M., Sudan, M.: Linearity testing in characteristic two. IEEE Transactions on Information Theory 42(6), 1781–1795 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bellare, M., Goldreich, O., Sudan, M.: Free bits, PCPs and non-approximability – towards tight results. SIAM J. Comput. 27(3), 804–915 (1998)CrossRefzbMATHGoogle Scholar
  5. 5.
    Blais, E.: Improved bounds for testing juntas. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 317–330. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Blais, E.: Testing juntas nearly optimally. In: Proc. 41st Symposium on Theory of Computing, pp. 151–158 (2009)Google Scholar
  7. 7.
    Blum, A.: Relevant examples and relevant features: thoughts from computational learning theory. In: AAAI Fall Symposium on ‘Relevance’ (1994)Google Scholar
  8. 8.
    Blum, A.: Learning a function of r relevant variables. In: Proc. 16th Conference on Computational Learning Theory, pp. 731–733 (2003)Google Scholar
  9. 9.
    Blum, A., Hellerstein, L., Littlestone, N.: Learning in the presence of finitely or infinitely many irrelevant attributes. J. Comp. Syst. Sci. 50(1), 32–40 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Blum, A., Langley, P.: Selection of relevant features and examples in machine learning. Artificial Intelligence 97(2), 245–271 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Blum, M., Luby, M., Rubinfeld, R.: Self-testing/correcting with applications to numerical problems. J. Comput. Syst. Sci. 47(3), 549–595 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Buhrman, H., Fortnow, L., Newman, I., Röhrig, H.: Quantum property testing. In: Proc. 14th Symp. on Discrete Algorithms, pp. 480–488 (2003)Google Scholar
  13. 13.
    Chen, V.: Query-Efficient dictatorship testing with perfect completeness. In: Goldreich, O. (ed.) Property Testing. LNCS, vol. 6390, pp. 276–279. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Chockler, H., Gutfreund, D.: A lower bound for testing juntas. Information Processing Letters 90(6), 301–305 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Diakonikolas, I., Lee, H.K., Matulef, K., Onak, K., Rubinfeld, R., Servedio, R.A., Wan, A.: Testing for concise representations. In: Proc. 48th Symposium on Foundations of Computer Science, pp. 549–558 (2007)Google Scholar
  16. 16.
    Efron, B., Stein, C.: The jackknife estimate of variance. Ann. of Stat. 9(3), 586–596 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Fischer, E., Kindler, G., Ron, D., Safra, S., Samorodnitsky, A.: Testing juntas. J. Comput. Syst. Sci. 68(4), 753–787 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. J. of the ACM 45(4), 653–750 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Goldreich, O., Ron, D.: Algorithmic aspects of property testing in the dense graphs model. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX–RANDOM 2009. LNCS, vol. 5687, pp. 520–533. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Goldreich, O., Ron, D.: Algorithmic aspects of property testing in the dense graphs model. In: Goldreich, O. (ed.) Property Testing. LNCS, vol. 6390, pp. 295–305. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Gonen, M., Ron, D.: On the benefits of adaptivity in property testing of dense graphs. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 525–539. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  22. 22.
    Guijarro, D., Tarui, J., Tsukiji, T.: Finding relevant variables in PAC model with membership queries. In: Watanabe, O., Yokomori, T. (eds.) ALT 1999. LNCS (LNAI), vol. 1720, pp. 313–322. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  23. 23.
    Lipton, R.J., Markakis, E., Mehta, A., Vishnoi, N.K.: On the Fourier spectrum of symmetric boolean functions with applications to learning symmetric juntas. In: Proc. 20th Conference on Computational Complexity, pp. 112–119 (2005)Google Scholar
  24. 24.
    Matulef, K., O’Donnell, R., Rubinfeld, R., Servedio, R.A.: Testing halfspaces. In: Proc. 19th Symp. on Discrete Algorithms, pp. 256–264 (2009)Google Scholar
  25. 25.
    Mossel, E., O’Donnell, R., Servedio, R.A.: Learning functions of k relevant variables. J. Comput. Syst. Sci. 69(3), 421–434 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Parnas, M., Ron, D., Samorodnitsky, A.: Testing basic boolean formulae. SIAM J. Discret. Math. 16(1), 20–46 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Rubinfeld, R., Sudan, M.: Self-testing polynomial functions efficiently and over rational domains. In: Proc. 3rd Symp. on Discrete Algorithms, pp. 23–32 (1992)Google Scholar
  28. 28.
    Servedio, R.: Testing by implicit learning: a brief survey. In: Goldreich, O. (ed.) Property Testing. LNCS, vol. 6390, pp. 197–210. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Eric Blais
    • 1
  1. 1.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations