Evolving the best known approximation to the Q function

Authors:
Dao Ngoc Phong;Nguyen Xuan Hoai;Robert Ian McKay;Constantin Siriteanu;Nguyen Quang Uy;Namyong Park
Affiliations:
Hanoi City Government, Hanoi, Vietnam;Hanoi University, Hanoi, Vietnam;Seoul National University, Seoul, South Korea;University of Hokkaido, Hokkaido, Japan;Military Technical Academy, Hanoi, Vietnam;Seoul National University, Seoul, South Korea
Venue:
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Year:
2012

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Abstract

The Gaussian Q-function is the integral of the tail of the Gaussian distribution; as such, it is important across a vast range of fields requiring stochastic analysis. No elementary closed form is possible, so a number of approximations have been proposed. We use a Genetic Programming (GP) system, Tree Adjoining Grammar Guided GP (TAG3P) with local search operators to evolve approximations of the Q-function in the form given by Benitez [1]. We found more accurate approximations than any previously published. This confirms the practical importance of local search in TAG3P.