A Novel Paradigm for Enhancing Linear Model Predictions across Multivariate Functions through Integration of CNNs

Abstract

Linear models have been a cornerstone in statistical data analysis, yet their inherent linearity often constrains their ability to extract nuanced patterns from complex datasets. This limitation poses a challenge in real-world applications where non-linearity prevails. In this research, we introduce an innovative methodology aimed at overcoming this deficiency. Leveraging the powerful non-linear modelling capabilities of Convolutional Neural Networks(CNNs), we augment the predictive capabilities of linear models. Through a systematic approach, we extend our findings to encompass specific classes of crucial multivariate functions. Our investigation primarily focuses on neural network architectures that integrate convolution (conv), Rectified Linear Unit (ReLU) activation functions, and max pooling layers. By harnessing the synergies of these components, we unveil a novel paradigm for enhancing linear model predictions, unlocking a wealth of potential applications across diverse domains. This research lays the foundation for a more robust and accurate predictive modelling framework that transcends the boundaries of conventional linear approaches.