Sparse PCA with False Discovery Rate Controlled Variable Selection
This addresses variable selection reliability in high-dimensional data analysis for fields like finance, though it is incremental as it builds on existing sparse PCA methods.
The paper tackles the problem of sparse PCA selecting irrelevant variables by proposing a formulation driven by false discovery rate (FDR) control, resulting in T-Rex PCA that eliminates sparsity parameter tuning and shows significant performance improvement in experiments.
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection. Sparse PCA algorithms are usually expressed as a trade-off between explained variance and sparsity of the loading vectors (i.e., number of selected variables). As a high explained variance is not necessarily synonymous with relevant information, these methods are prone to select irrelevant variables. To overcome this issue, we propose an alternative formulation of sparse PCA driven by the false discovery rate (FDR). We then leverage the Terminating-Random Experiments (T-Rex) selector to automatically determine an FDR-controlled support of the loading vectors. A major advantage of the resulting T-Rex PCA is that no sparsity parameter tuning is required. Numerical experiments and a stock market data example demonstrate a significant performance improvement.