Extremely Accurate Symbolic Regression for Large Feature Problems

Abstract

As symbolic regression (SR) has advanced into the early stages of commercial exploitation, the poor accuracy of SR, still plaguing even the most advanced commercial packages, has become an issue for early adopters. Users expect to have the correct formula returned, especially in cases with zero noise and only one basis function with minimally complex grammar depth.

At a minimum, users expect the response surface of the SR tool to be easily understood, so that the user can know apriori on what classes of problems to expect excellent, average, or poor accuracy. Poor or unknown accuracy is a hinderence to greater academic and industrial acceptance of SR tools.

In a previous paper, we published a complex algorithm for modern symbolic regression which is extremely accurate for a large class of Symbolic Regression problems. The class of problems, on which SR is extremely accurate, was described in detail. This algorithm was extremely accurate, on a single processor, for up to 25 features (columns); and, a cloud configuration was used to extend the extreme accuracy up to as many as 100 features.

While the previous algorithm’s extreme accuracy for deep problems with a small number of features (25–100) was an impressive advance, there are many very important academic and industrial SR problems requiring from 100 to 1000 features.

In this chapter we extend the previous algorithm such that high accuracy is achieved on a wide range of problems, from 25 to 3000 features, using only a single processor. The class of problems, on which the enhanced algorithm is highly accurate, is described in detail. A definition of extreme accuracy is provided, and an informal argument of highly SR accuracy is outlined in this chapter.

The new enhanced algorithm is tested on a set of representative problems. The enhanced algorithm is shown to be robust, performing well even in the face of testing data containing up to 3000 features.