Comparison of OLS and NLS to fit Transformation-Interaction-Rational expressions

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Author(s):	de Franca, Fabricio Olivetti ; Buchberger, B ; Marin, M ; Negru, V ; Zaharie, D Total Authors: 5
Document type:	Journal article
Source:	2022 24TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND NUMERIC ALGORITHMS FOR SCIENTIFIC COMPUTING, SYNASC; v. N/A, p. 4-pg., 2022-01-01.
Abstract
Transformation-Interaction-Rational is a representation for Symbolic Regression created with the intent to constrain the search space of mathematical expressions with only simple models. In short, this representation is a rational of two linear models with transformed variables. Even though the representation makes the model nonlinear w.r.t. its numerical parameters, it is possible to rewrite the expression such that the parameters become linear and, thus, can be adjusted using the Ordinary Least Squares method, that guarantees the global optima solution. But, when we are working with a noisy data set, the reparametrization procedure may skew the noise distribution leading to an incorrect value for the numerical parameters. In this work, we test and compare the use of Ordinary Least Square and a non-linear optimization in simulated benchmarks with the presence of noise. The results show evidence that OLS is robust to noise and always returns a similar solution to the non-linear optimization algorithm. (AU)

FAPESP's process:	21/12706-1 - Shape-constrained symbolic regression
Grantee:	Fabricio Olivetti de França
Support Opportunities:	Scholarships abroad - Research