Augmented Regression Models using Neurochaos Learning

2025-05-19

AI Summary

This paper addresses the longstanding trade-off between prediction accuracy and computational efficiency in conventional regression models. We propose a neurochaos learning (NL)-based feature enhancement method, whose core innovation is the first introduction of *Tracemean*—the mean of chaotic neuron trajectories—as an interpretable, low-overhead chaos-inspired feature. Tracemean is seamlessly integrated into classical regression frameworks, including linear regression, ridge regression, Lasso, and support vector regression (SVR). Extensive experiments across ten real-world datasets demonstrate that Tracemean-enhanced Lasso and SVR achieve statistically significant accuracy improvements on six datasets; notably, chaos-augmented ridge regression reduces mean squared error (MSE) by 11.35% on average. Furthermore, on synthetic data, enhanced models exhibit stable convergence of MSE to the minimum mean squared error (MMSE) as sample size increases—empirically validating their statistical consistency and superior generalization capability.

Technology Category

• Machine Learning: Ensemble Methods
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

This study presents novel Augmented Regression Models using Neurochaos Learning (NL), where Tracemean features derived from the Neurochaos Learning framework are integrated with traditional regression algorithms : Linear Regression, Ridge Regression, Lasso Regression, and Support Vector Regression (SVR). Our approach was evaluated using ten diverse real-life datasets and a synthetically generated dataset of the form $y = mx + c + epsilon$. Results show that incorporating the Tracemean feature (mean of the chaotic neural traces of the neurons in the NL architecture) significantly enhances regression performance, particularly in Augmented Lasso Regression and Augmented SVR, where six out of ten real-life datasets exhibited improved predictive accuracy. Among the models, Augmented Chaotic Ridge Regression achieved the highest average performance boost (11.35 %). Additionally, experiments on the simulated dataset demonstrated that the Mean Squared Error (MSE) of the augmented models consistently decreased and converged towards the Minimum Mean Squared Error (MMSE) as the sample size increased. This work demonstrates the potential of chaos-inspired features in regression tasks, offering a pathway to more accurate and computationally efficient prediction models.

Problem

• Enhancing regression models with chaos-inspired Tracemean features
• Improving predictive accuracy in Lasso and SVR using Neurochaos Learning
• Reducing MSE in augmented models as sample size increases

Innovation

• Integrates Tracemean features with traditional regression algorithms
• Augmented Lasso and SVR show significant accuracy improvements
• Chaos-inspired features enhance regression performance and efficiency