用混沌神经特征增强传统回归模型，提升预测精度。
Augmented Regression Models using Neurochaos Learning
- 从混沌神经网络提取轨迹均值特征，融合进经典回归算法。
- 六组真实数据集预测准确率提升，增广岭回归平均增益11.35%。
- 适合追求高精度、低计算开销的回归任务研究者使用。
本研究提出基于神经混沌学习（NL）的增强型回归模型，将NL框架中神经元混沌轨迹的迹均值（Tracemean）特征与线性回归、岭回归、套索回归及支持向量回归（SVR）结合。在十个真实世界数据集和一个形如 $y = mx + c + ε$ 的合成数据集上评估，结果表明引入Tracemean特征显著提升回归性能，尤其在增广套索回归与增广SVR中，六组真实数据集预测准确率提高。其中，增广混沌岭回归实现最高平均性能提升（11.35%）。合成数据实验显示，随着样本量增加，增广模型的均方误差（MSE）持续下降并趋近于最小均方误差（MMSE）。该工作验证了混沌启发特征在回归任务中的潜力，为构建更精准、高效预测模型提供新路径。
原文摘要 · Abstract (English)
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 $y = mx + c + ε$. 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.
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