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This paper proposes a hybrid basis function construction method (GP-RVM) forSymbolic Regression problem, which combines an extended version of GeneticProgramming called Kaizen Programming and Relevance Vector Machine to evolve anoptimal set of basis functions. Different from traditional evolutionaryalgorithms where a single individual is a complete solution, our methodproposes a solution based on linear combination of basis functions built fromindividuals during the evolving process. RVM which is a sparse Bayesian kernelmethod selects suitable functions to constitute the basis. RVM determines theposterior weight of a function by evaluating its quality and sparsity. Thesolution produced by GP-RVM is a sparse Bayesian linear model of thecoefficients of many non-linear functions. Our hybrid approach is focused onnonlinear white-box models selecting the right combination of functions tobuild robust predictions without prior knowledge about data. Experimentalresults show that GP-RVM outperforms conventional methods, which suggest thatit is an efficient and accurate technique for solving SR. The computationalcomplexity of GP-RVM scales in $O( M^{3})$, where $M$ is the number offunctions in the basis set and is typically much smaller than the number $N$ oftraining patterns.

GP-RVM: Genetic Programing-based Symbolic Regression Using Relevance Vector Machine