Abstract Expression Grammar Symbolic Regression

Abstract

This chapter examines the use of Abstract Expression Grammars to perform the entire Symbolic Regression process without the use of Genetic Programming per se. The techniques explored produce a symbolic regression engine which has absolutely no bloat, which allows total user control of the search space and output formulas, which is faster, and more accurate than the engines produced in our previous papers using Genetic Programming. The genome is an all vector structure with four chromosomes plus additional epigenetic and constraint vectors, allowing total user control of the search space and the final output formulas. A combination of specialized compiler techniques, genetic algorithms, particle swarm, aged layered populations, plus discrete and continuous differential evolution are used to produce an improved symbolic regression sytem. Nine base test cases, from the literature, are used to test the improvement in speed and accuracy. The improved results indicate that these techniques move us a big step closer toward future industrial strength symbolic regression systems. While the techniques, described in detail in (Korns, 2009), produce a symbolic regression system of breadth and strength, lack of user control of the search space, bloated unreadable output formulas, accuracy, and slow convergence speed are all issues keeping an industrial strength symbolic regression system tantalizingly out of reach. In this chapter abstract expression grammars become the main focus and are promoted as the sole means of performing symbolic regression. Using the nine base test cases from (Korns, 2007) as a training set, to test for improvements in accuracy, we constructed our symbolic regression system using these important techniques:Abstract expression grammars Universal abstract goal expression Standard single point vector-based mutation Standard two point vector-based cross over Continuous vector differential evolution Discrete vector differential evolution Continuous particle swarm evolution Pessimal vertical slicing and out-of-sample scoring during training Age-layered populations User defined epigenetic factors User defined constraints

Accuracy in Symbolic Regression

“…The basics of Abstract Expression Grammars and Universal Abstract Expressions are described in (Korns, 2010). Reviewing Abstract Expression Grammars is strongly advised before continuing with this chapter.…”

“…In (Korns, 2010) a number of important concepts are developed including: abstract expression grammars (AEG), universal abstract expressions, a new pro-totype search specification language inspired by the SQL/database-search relationship, and the concept of epigenome constraints to focus the search process in specific island populations. In this chapter, we will employ these concepts to help solve previously intractable problems.…”

“…There is at least one very well done open source symbolic regression package available for free download http://ccsl.mae.cornell.edu/eureqa. In addition to our own ARC system (Korns, 2010), currently used internally for massive (million row) financial data nonlinear regressions, there are a number of other mature symbolic regression packages currently used in industry including (Smits et al, 2010) and (Castillo et al, 2010). Plus there is an interesting work in progress by (McConaghy et al, 2009).…”

Extremely Accurate Symbolic Regression for Large Feature Problems

“…During the writing of Korns (2010Korns ( , 2011Korns ( , 2012Korns ( , 2013 a high level regression search language was developed called RQL. RQL was inspired by the database search language SQL.…”

Kaizen programming

“…GP has been employed to automatically produce codes to solve (see [13]): curve-fitting, data modelling, symbolic regression, image and signal processing, financial trading, time series, industrial process control, bioinformatics, among others. Despite its successful application in several domains, there are some known issues with GP and related algorithms [11,7], for instance, bloat, lack of heuristics, slow speed (large population size), and low success rate.…”