Large-Scale, Time-Constrained Symbolic Regression-Classification

Symbolic regression using abstract expression grammars

“…10.1 hyper: y = 1.57 + (1.57*tanh(cube(x1))) -(39.34*tanh(cube(x2))) + (2.13*tanh(cube(x3))) + (46.59*tanh(cube(x4))) + (11.54*tanh(cube(x5))) Using the nonlinear regression system described in [2] [3], we construct an X matrix 10,000 by 5, filled with random numbers between -50 and +50, and run the "hyper" training model (10.1) on each row of X to create the Y dependent vector. When we request (quickly training for only 25 generations) the nonlinear regression system to optimize, f = p1, the following results are returned.…”

“…While some of the concepts of abstract expression grammars have been implemented in [2] [3], at this time there appear to be no nonlinear regression systems in which all of these concepts are used. There is little benefit from keeping such valuable, yet disparate, algorithms as GA, GP, Particle Swarm, Differential Evolution, Support Vectors, Neural Nets, and even Gaussian Regression, separated, in isolation, and prevented from working together smoothly.…”

“…In testing nonlinear regression using abstract expression grammars we borrow the "hyper" test case published in [2].…”

“…The output of a nonlinear regression system will be a program object (which we will hereinafter call an Estimator Agent), f, such that invoking f on each row of X produces an estimate vector, EY, which minimizes the normalized least square error between EY and Y. General nonlinear regression systems can be constructed using genetic programming methods [2] [3] [4] [6].…”

“…In fact abstract expression grammars are currently being used inside a symbolic regression system for large scale symbolic regression [2] [3].…”