Distance Correlation Based Feature Selection in Random Forest
The Pearson correlation coefficient is a commonly used measure of correlation, but it has limitations as it only measures the linear relationship between two numerical variables. In 2007, Szekely et al. introduced the distance correlation, which measures all types of dependencies between random vectors X and Y in arbitrary dimensions, not just the linear ones. In this thesis, we propose a filter method that utilizes distance correlation as a criterion for feature selection in Random Forest regression. We conduct extensive simulation studies to evaluate its performance compared to existing methods under various data settings, in terms of the prediction mean squared error. The results show that our proposed method is competitive with existing methods and outperforms all other methods in high-dimensional (p > 300) nonlinearly related data sets. The applicability of the proposed method is also illustrated by two real data applications.