Improving the performance of independent component regression

In this study, we aim to comprehensively explore the application of principal component analysis (PCA) and independent component analysis (ICA), considering their practical utility. We compare these two methods theoretically and practically, using both real data and simulated data. PCA and ICA algorithms are often treated as black boxes, therefore they are often seen as complex algorithms. In this research, we’ll break down some of the theory behind ICA. Subsequently, we compare principal component regression (PCR) and independent component regression (ICR) in both real and simulated datasets. Our objectives include data analysis and explanation of the superiority of each method (ICA and PCA) across different datasets. We will propose solutions to improve the performance of ICR and PCR regressions for datasets with structures suited to ICA and PCA.