Logistic regression by means of evolutionary radial basis function neural networks

Area of Science:

• Machine Learning
• Statistical Modeling
• Artificial Intelligence

Background:

• Traditional logistic regression models often struggle with complex, nonlinear relationships in data.
• Radial Basis Function Neural Networks (RBFNNs) offer a powerful way to model nonlinearities but can be complex to optimize.
• Integrating RBF transformations into logistic regression provides a hybrid approach to enhance predictive accuracy.

Purpose of the Study:

• To propose a novel hybrid multilogistic methodology combining logistic regression with radial basis function (RBF) covariates.
• To develop an efficient coefficient estimation process using evolutionary programming (EP) and maximum likelihood optimization.
• To introduce and evaluate a simplelogistic initial-RBF regression (SLIRBF) method for automatic covariate selection and improved classification.

Main Methods:

• A three-step process involving evolutionary programming (EP) for RBFNN optimization, covariate space augmentation with RBF transformations, and maximum likelihood estimation for model coefficients.
• Implementation of two multilogistic regression algorithms: one using all initial and RBF covariates, and another (SLIRBF) employing incremental construction and cross-validation for automatic covariate selection.
• Optimization of a regularization parameter for both proposed methods.

Main Results:

• The proposed hybrid methodology, particularly SLIRBF, was tested on 18 benchmark classification problems and two agronomical datasets.
• SLIRBF models demonstrated competitive performance against standard multilogistic regression, RBFNNs from EP, and other probabilistic classifiers.
• Statistical significance measures indicated that SLIRBF achieved state-of-the-art results in classification accuracy.

Conclusions:

• The hybrid multilogistic methodology effectively enhances logistic regression by incorporating RBF covariates.
• The SLIRBF approach offers an efficient and automated way to build high-performing classification models.
• This research advances the field by providing a robust and statistically significant method for complex classification problems.