ABSTRACT
This paper presents a search algorithm for finding functions that are highly correlated with an arbitrary set of data. The functions found by the search can be used to approximate the unknown function that generated the data. A special case of this approach is a method for learning Fourier representations. Empirical results demonstrate that on typical real-world problems the most highly correlated functions can be found very quickly, while combinations of these functions provide good approximations of the unknown function.
- Blake, C., & Merz, C. (1998). UCI repository of machine learning databases.Google Scholar
- Drake, A., & Ventura, D. (2005). Comparing high-order boolean features. Proceedings of the 8th Joint Conference on Information Sciences, to appear.Google Scholar
- Freund, Y., & Schapire, R. (1996). Experiments, with a new boosting algorithm. Proceedings of the 13th International Conference on Machine Learning, 55, 148--156.Google Scholar
- Jackson, J. (1997). An efficient membership-query algorithm for learning dnf with respect to the uniform distribution. Journal of Computer and System Sciences, 55, 414--440. Google ScholarDigital Library
- Kushilevitz, E., & Mansour, Y. (1993). Learning decision trees using the fourier spectrum. SIAM Journal on Computing, 22, 1331--1348. Google ScholarDigital Library
- Linial, N., Mansour, Y., & Nisan, N. (1993). Constant depth circuits, fourier transform, and learnability. Journal of the ACM, 40, 607--620. Google ScholarDigital Library
- Mansour, Y., & Sahar, S. (2000). Implementation issues in the fourier transform algorithm. Machine Learning, 14, 5--33. Google ScholarDigital Library
- A practical generalization of Fourier-based learning
Recommendations
Fourier transforms and bent functions on finite groups
Let G be a finite nonabelian group. Bent functions on G are defined by the Fourier transforms at irreducible representations of G. We introduce a dual basis $${\widehat{G}}$$G^, consisting of functions on G determined by its unitary irreducible ...
Value function approximation in reinforcement learning using the fourier basis
AAAI'11: Proceedings of the Twenty-Fifth AAAI Conference on Artificial IntelligenceWe describe the Fourier basis, a linear value function approximation scheme based on the Fourier series. We empirically demonstrate that it performs well compared to radial basis functions and the polynomial basis, the two most popular fixed bases for ...
Fourier transforms on finite group actions and bent functions
AbstractHighly nonlinear functions (bent functions, perfect nonlinear functions, etc.) on finite fields and finite (abelian or nonabelian) groups have been studied in numerous papers. As a generalization of bent functions on finite groups, bent functions ...
Comments