Random Polynomial Neural Networks: Analysis and Design.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Neuroscience

Background:

• Polynomial Neural Networks (PNNs) are effective for modeling complex nonlinear systems.
• Traditional PNNs utilize polynomial neurons (PNs) that can be sensitive to outliers and prone to overfitting.
• Random Forests (RFs) offer ensemble learning benefits, including robustness and variable importance estimation.

Purpose of the Study:

• To introduce Random Polynomial Neural Networks (RPNNs) by integrating RF architecture into PNNs.
• To enhance the robustness and accuracy of nonlinear system modeling.
• To address limitations of conventional PNNs, such as outlier sensitivity and overfitting.

Main Methods:

• Developed Random Polynomial Neurons (RPNs) based on RF architecture, generalizing PNs.
• Utilized polynomial target variables for prediction in RPNs, deviating from direct target variable use in decision trees.
• Employed the correlation coefficient for RPN selection within layers, instead of conventional performance indices.
• Optimized RPNN parameters using Particle Swarm Optimization (PSO).

Main Results:

• RPNs demonstrated insensitivity to outliers.
• RPNs provided insights into input variable importance post-training.
• The RF structure in RPNs effectively alleviated the overfitting problem.
• RPNNs combined the high accuracy of RF ensemble learning with PNN's ability to model high-order nonlinear relations.
• Experimental results on benchmark datasets showed RPNNs outperformed existing state-of-the-art models.

Conclusions:

• RPNNs offer a robust and accurate approach for modeling complex nonlinear systems.
• The integration of RF and PNN architectures yields significant advantages over conventional methods.
• RPNNs represent a promising advancement in machine learning for complex system modeling.