- 1.Dana Angluin. Learning regular sets from queries and counterexamples. Information and Computation, 75:87-106, November 1987. Google ScholarDigital Library
- 2.Sigal Ar, Richard J. Lipton, Ronitt Rubinfeld, and Madhu Sudan. Reconstructing algebraic functions from mixed data. In 33rd Annual Symposium on Foundations of Computer Science, pages 503-512, October 1992.Google ScholarDigital Library
- 3.Michael Ben-Or and Prasoon Tiwari. A deterministic algorithm for sparse multivariate polynomial interpolation. In Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pages 301-309, May 1988. Google ScholarDigital Library
- 4.Avrim Blum. Learning boolean functions in an infinite attribute space. Machine Learning, 9(4):373-386, 1992. Google ScholarDigital Library
- 5.Avrim Blum and Mona Singh. Learning functions of k terms. In Proceedings of the Third Annual Workshop on Computational Learning Theory, pages 144-153, August 1990. Google ScholarDigital Library
- 6.Anselm Blumer, Andrzej Ehrenfeucht, David Haussler, and Manfred K. Warmuth. Learnability and the Vapnik- Chervonenkis dimension. Journal of the Association for Computing Machinery, 36(4):929-965, October 1989. Google ScholarDigital Library
- 7.Nader H. Bshouty. Exact learning. Unpublished manuscript, 1993.Google Scholar
- 8.Michael Clausen, Andreas Dress, Johannes Grabmeier, and Marek Karpinski. On zero-testing and interpolation of k-sparse multivariate polynomials over finite fields. Theoretical Computer Science, 84:151-164, 1991. Google ScholarDigital Library
- 9.Paul Fischer and Hans Ulrich Simon. On learning ring-sum-expansions. SIAM Journal on Computing, 21(1): 181-192, February 1992. Google ScholarDigital Library
- 10.PeterGemmell and Madhu Sudan. Highly resilient correctors for polynomials. Information Processing Letters, 43(4): 169-174, September 1992. Google ScholarDigital Library
- 11.Dima Yu. Grigoriev, Marek Karpinski, and Michael E Singers. Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields. SIAM Journal on Computing, 19(6): 1059-1963, December 1990. Google ScholarDigital Library
- 12.David Haussler. Decision theoretic generalizations of the PAC model for neural net and other learning applications. Information and Computation, 100(1):78-150, 1992. Google ScholarDigital Library
- 13.Lisa Hellerstein and Manfred Warmuth. InterpolatingGoogle Scholar
- 14.I.N. Herstein. Topics in Algebra. Wiley, second edition, 1975.Google Scholar
- 15.Eyal Kushilevitz and Yishay Mansour. Learning decision trees using the fourier spectrum. In Proceedings of the Twenty Third Annual ACM Symposium on Theory of Computing, pages 455--464, May 1991. Google ScholarDigital Library
- 16.Yishay Mansour. Randomized interpolation and approximation of sparse polynomials, In Automata. Languages and Programming: 19th International Colloquium, pages 261-272, July 1992. Google ScholarDigital Library
- 17.Ron M. Roth and Gyora M. Benedek. Interpolation and approximation of sparse multivariate polynomials over GF(2). SIAM Journal on Computing, 20(2):291-314, April 1991. Google ScholarDigital Library
- 18.L. G. Valiant. A theory of the learnable. Communications of the ACM, 27(11): 1134-1142, November 1984. Google ScholarDigital Library
- 19.Richard Zippel. Probabilistic algorithms for sparse polynomials. In Symbolic and Algebraic Computation, pages 216-226. Springer-Verlag, June 1979. Google ScholarDigital Library
- 20.Richard Zippel. Interpolating polynomials from their values. Journal of SymboUc Computation, 9:375--403, 1990. Google ScholarDigital Library
Index Terms
- Learning sparse multivariate polynomials over a field with queries and counterexamples
Recommendations
Learning Sparse Multivariate Polynomials over a Field with Queries and Counterexamples
We consider the problem of learning a polynomial over an arbitrary fieldFdefined on a set of boolean variables. We present the first provably effective algorithm for exactly identifying such polynomials using membership and equivalence queries. Our ...
Extracting sparse factors from multivariate integral polynomials
In this paper we present a new algorithm for extracting sparse factors from multivariate integral polynomials. The method hinges on a new type of substitution, which reduces multivariate integral polynomials to bivariate polynomials over finite fields ...
Symbolic-numeric sparse interpolation of multivariate polynomials
ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computationWe consider the problem of sparse interpolation of an approximate multivariate black-box polynomial in floating-point arithmetic. That is, both the inputs and outputs of the black-box polynomial have some error, and all numbers are represented in ...
Comments