  In high-dimensional data analysis, such as financial index tracking or
biomedical applications, it is crucial to select the few relevant variables
while maintaining control over the false discovery rate (FDR). In these
applications, strong dependencies often exist among the variables (e.g., stock
returns), which can undermine the FDR control property of existing methods like
the model-X knockoff method or the T-Rex selector. To address this issue, we
have expanded the T-Rex framework to accommodate overlapping groups of highly
correlated variables. This is achieved by integrating a nearest neighbors
penalization mechanism into the framework, which provably controls the FDR at
the user-defined target level. A real-world example of sparse index tracking
demonstrates the proposed method's ability to accurately track the S&P 500
index over the past 20 years based on a small number of stocks. An open-source
implementation is provided within the R package TRexSelector on CRAN.
