基于神经混沌学习的增强回归模型
Augmented Regression Models using Neurochaos Learning
- Department of Mathematics（数学系）
- Amrita Vishwa Vidyapeetham（阿米塔维莎维达佩特姆大学）
- Complex Systems Programme（复杂系统计划）
- National Institute of Advanced Studies（国家高级研究所）
- Indian Institute of Science（印度科学研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出将神经混沌学习的Tracemean特征与传统回归算法结合的增强回归模型，经10个真实数据集和合成数据集验证，可显著提升回归性能，为更高效准确的预测模型提供新思路。
AI中文摘要：
本研究提出了基于神经混沌学习（Neurochaos Learning, NL）的新型增强回归模型，将源自神经混沌学习框架的Tracemean特征与传统回归算法（线性回归、岭回归、Lasso回归和支持向量回归（SVR））相结合。我们使用10个不同的真实数据集以及一个形式为$y = mx + c + ε$的合成生成数据集对该方法进行了评估。结果表明，引入Tracemean特征（NL架构中神经元的混沌神经轨迹的均值）可显著提升回归性能，尤其是在增强Lasso回归和增强SVR中，10个真实数据集中有6个的预测精度得到了提升。在所有模型中，增强混沌岭回归实现了最高的平均性能提升（11.35%）。此外，在模拟数据集上的实验表明，随着样本量增加，增强模型的均方误差（MSE）持续下降并收敛至最小均方误差（MMSE）。本研究证明了混沌启发特征在回归任务中的潜力，为构建更准确、计算更高效的预测模型提供了路径。
英文摘要：
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.
