Beyond Noise: A Hypothesis Testing Approach to Robust Feature Selection

Feature selection remains difficult in modern high-dimensional settings, and established methods such as Boruta and Recursive Feature Elimination are either computationally costly or lack a statistically justified stopping criterion for their importance scores. A common heuristic adds random noise features and retains any predictor ranking above the strongest one, but this rule is purely ad hoc. We introduce a method that keeps the noise-augmentation idea while grounding it in theory: each feature's importance is tested against the maximum noise importance using a non-parametric bootstrap hypothesis test, with statistical derivations supporting the algorithm's design. On controlled simulations, the method recovers true signal more consistently than Boruta and Knockoff-based procedures; on diverse real-world datasets, it outperforms Boruta, RFE, and Extra Trees. The result is a robust, principled selector that yields reliable inference, improved prediction, and efficient computation.