An invariance principle for polytopes

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2010, Pages 543-552

  Harsha, Prahladh ^a   Klivans, Adam ^b   Meka, Raghu ^b  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

agnostic learning; average sensitivity; contingency tables; invariance principles; limit theorems; noise sensitivity; polytopes; pseudorandom generators

Indexed keywords

AGNOSTIC LEARNING; CONTINGENCY TABLE; INVARIANCE PRINCIPLE; LIMIT THEOREM; NOISE SENSITIVITY; POLYTOPES; PSEUDORANDOM GENERATORS;

ACOUSTIC NOISE; INTEGER PROGRAMMING; LEARNING ALGORITHMS; NOISE GENERATORS; POLYNOMIAL APPROXIMATION; TOPOLOGY;

COMPUTATION THEORY;

EID: 77954805501     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1806689.1806764     Document Type: Conference Paper

References (37)

1. N. AILON and B. CHAZELLE. Approximate nearest neighbors and the fast Johnson Lindenstrauss transform. In STOC, pages 557-563. 2006.
2. k. Lithuanian Mathematical Journal, 30(3):223-230, July 1990.
3. VIDMANTAS K. BENTKUS. -. On the dependence of the BerryâǍ Ş-Esseen bound on dimension. Journal of Statistical Planning and Inference, 113(2):385-402, May 2003.
4. ITAI BENJAMINI, GIL KALAI, and ODED SCHRAMM. Noise sensitivity of Boolean functions and applications to percolation. Inst. Hautes Études Sci. Publ. Math., 90(1):5-43, 1999. arXiv:math/9811157.
5. MATTHIAS BECK and SINAI ROBINS. Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra. Undergraduate Texts in Mathematics. Springer, 1st edition, 2007.
6. ALEXANDER BARVINOK and ELLEN VEOMETT. The computational complexity of convex bodies. In JACOB E. GOODMAN, JÁNOS PACH, and RICHARD POLLACK, eds., Surveys on Discrete and Computational Geometry: Twenty Years Later, volume 453 of Contemporary Mathematics, pages 117-137. AMS, 2008. arXiv:math/0610325.
7. MARY CRYAN and MARTIN E. DYER. A polynomial-time algorithm to approximately count contingency tables when the number of rows is constant. J. Comp. Sys. Sci., 67(2):291-310, 2003.
8. I. DIAKONIKOLAS, P. HARSHA, A. KLIVANS, R. MEKA, P. RAGHAVENDRA, R. SERVEDIO, and L. TAN. Bounding the average sensitivity and noise sensitivity of polynomial threshold functions. In STOC, to appear. 2010.
9. ILIAS DIAKONIKOLAS, DANIEL M. KANE, and JELANI NELSON. Bounded independence fools degree-2 threshold functions, 2009. arXiv:0911.3389.
10. M. E. DYER. Approximate counting by dynamic programming. In STOC, pages 693-699. 2003.
11. WILLIAM FELLER. An Introduction to Probability Theory and Its Applications, Volume 2. Wiley, 2nd edition, 1971.
12. P. GOPALAN, R. O'DONNELL, Y. WU, and D. ZUCKERMAN. Fooling functions of halfspaces under product distributions. In CCC, to appear. 2010.
13. MICHEL X. GOEMANS and DAVID P. WILLIAMSON. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM, 42(6):1115-1145, 1995. (Preliminary version in 26th STOC, 1994).
14. JOHAN HÅSTAD. Some optimal inapproximability results. J. ACM, 48(4):798-859, July 2001. (Preliminary Version in 29th STOC, 1997).
15. RUSSELL IMPAGLIAZZO, NOAM NISAN, and AVI WIGDERSON. Pseudorandomness for network algorithms. In STOC, pages 356-364. 1994.
16. MARK JERRUM and ALISTAIR SINCLAIR. The Markov chain Monte Carlo method: An approach to approximate counting and integration. In DORIT S. HOCHBAUM, ed., Approximation Algorithms for NP-hard Problems. PWS Publishing Company, 1997.
17. GIL KALAI. Noise sensitivity and chaos in social choice theory. Technical Report 399, Center for Rationality and Interactive Decision Theory, Hebrew University of Jerusalem, 2005.
18. JEFF KAHN, GIL KALAI, and NATHAN LINIAL. The influence of variables on Boolean functions (extended abstract). In FOCS, pages 68-80. 1988.
19. SUBHASH KHOT, GUY KINDLER, ELCHANAN MOSSEL, and RYAN O'DONNELL. Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? SIAM J. Computing, 37(1):319-357, 2007.
20. ADAM TAUMAN KALAI, ADAM R. KLIVANS, YISHAY MANSOUR, and ROCCO A. SERVEDIO. Agnostically learning halfspaces. SIAM J. Computing, 37(6):1777-1805, 2008. (Preliminary version in 46th FOCS, 2005).
21. ADAM R. KLIVANS, RYAN O'DONNELL, and ROCCO A. SERVEDIO. Learning intersections and thresholds of halfspaces. J. Comp. Sys. Sci., 68(4):808-840, 2004. (Preliminary version in 43rd FOCS, 2002).
22. ADAM R. KLIVANS, RYAN O'DONNELL, and ROCCO A. SERVEDIO. -. Learning geometric concepts via Gaussian surface area. In FOCS, pages 541-550. 2008.
23. NATHAN LINIAL, YISHAY MANSOUR, and NOAM NISAN. Constant depth circuits, Fourier transform, and learnability. J. ACM, 40(3):607-620, 1993. (Preliminary version in 30th FOCS, 1989).
24. YISHAY MANSOUR. Learning Boolean functions via the Fourier transform. In VWANI P. ROYCHOWDHURY, KAI-YEUNG SIU, and ALON ORLITSKY, eds., Theoretical Advances in Neural Computation and Learning, pages 391-424. Kluwer Academic Publishers, 1994.
25. SANJEEV MAHAJAN and RAMESH HARIHARAN. Derandomizing approximation algorithms based on semidefifinite programming. SIAM J. Computing, 28(5):1641-1663, 1999. (Preliminary version in 36th FOCS, 1995).
26. ELCHANAN MOSSEL, RYAN O'DONNELL, and KRZYSZTOF OLESZKIEWICZ. Noise stability of functions with low in.uences invariance and optimality. In FOCS, pages 21-30. 2005. arXiv:math/0503503.
27. ELCHANAN MOSSEL. Gaussian bounds for noise correlation of functions and tight analysis of long codes. In FOCS, pages 156-165. 2008. arXiv:math/0703683.
28. R. MEKA and D. ZUCKERMAN. Pseudorandom generators for polynomial threshold functions. In STOC,to appear. 2010. arXiv:0910.4122.
29. n with respect to a Gaussian measure. In Geometric Aspects of Functional Analysis (Israel Seminar 2001-2002), volume 1807/2003 of Lecture Notes in Mathematics, pages 169-187. Springer, 2003.
30. JOSEPH NAOR and MONI NAOR. Small-bias probability spaces: Efficient constructions and applications. SIAM J. Computing, 22(4):838-856, August 1993. (Preliminary Version in 22nd STOC, 1990).
31. RYAN O'DONNELL. Hardness amplification within NP. J. Comp. Sys. Sci., 69(1):68-94, 2004. (Preliminary version in 34th STOC, 2002).
32. RYAN O'DONNELL. -. Some topics in analysis of Boolean functions. In STOC, pages 569-578. 2008. eccc:TR08-055.
33. YUVAL PERES. Noise stability of weighted majority, 2004. arXiv:math/0412377.
34. VYGANTAS PAULAUSKAS and ALFREDAS RAČKAUSKAS. Approximation Theory in the Central Limit Theorem: Exact Results in Banach Spaces. Kluwer Academic Publishers, 1989. (Translated from Russian).
35. YAOYUN SHI. Lower bounds of quantum black-box complexity and degree of approximating polynomials by influence of Boolean variables. Inf. Process. Lett., 75(1-2):79-83, 2000. arXiv:quant-ph/9904107.
36. PAWEL WOLFF. Hypercontractivity of simple random variables. Studia Math, 180(3):219-236, 2007.
37. GÜNTER M. ZIEGLER. Lectures on polytopes, volume 152 of Graduate texts in Mathematics. Springer, 1995.