Accuracy in Symbolic Regression

Abstract

This chapter asserts that, in current state-of-the-artsymbolic regression engines, accuracy is poor. That isto say that state-of-the-art symbolic regressionengines return a champion with good fitness; however,obtaining a champion with the correct formula is notforthcoming even in cases of only one basis functionwith minimally complex grammar depth.Ideally, users expect that for test problems createdwith no noise, using only functions in the specifiedgrammar, with only one basis function and some minimalgrammar depth, that state-of-the-art symbolicregression systems should return the exact formula (orat least an isomorph) used to create the test data.Unfortunately, this expectation cannot currently beachieved using published state-of-the-art symbolicregression techniques.Several classes of test formulas, which proveintractable, are examined and an understanding of whythey are intractable is developed. Techniques inAbstract Expression Grammars are employed to renderthese problems tractable, including manipulation of theepigenome during the evolutionary process, togetherwith breeding of multiple targeted epigenomes inseparate population islands.A selected set of currently intractable problems areshown to be solvable, using these techniques, and aproposal is put forward for a discipline-wide programof improving accuracy in state-of-the-art symbolicregression systems.