Accuracy in Symbolic Regression

Abstract

This chapter asserts that, in current state-of-the-art symbolic regression engines, accuracy is poor. That is to say that state-of-the-art symbolic regression engines return a champion with good fitness; however, obtaining a champion with the correct formula is not forthcoming even in cases of only one basis function with minimally complex grammar depth. Ideally, users expect that for test problems created with no noise, using only functions in the specified grammar, with only one basis function and some minimal grammar depth, that state-of-the-art symbolic regression systems should return the exact formula (or at least an isomorph) used to create the test data. Unfortunately, this expectation cannot currently be achieved using published state-of-the-art symbolic regression techniques. Several classes of test formulas, which prove intractable, are examined and an understanding of why they are intractable is developed. Techniques in Abstract Expression Grammars are employed to render these problems tractable, including manipulation of the epigenome during the evolutionary process, together with breeding of multiple targeted epigenomes in separate population islands. Aselected set of currently intractable problems are shown to be solvable, using these techniques, and a proposal is put forward for a discipline-wide program of improving accuracy in state-of-the-art symbolic regression systems.