General theory for LAMPS under correlated features

Develop a full-fledged theory characterizing the feature-selection performance of LOCO-guided Adaptive Minipatch Sampling (LAMPS) under general feature correlation.

Background

The paper establishes exact feature-selection guarantees for LAMPS primarily under sparse additive models with independent features. It also analyzes a highly simplified correlated setting involving one signal feature and one correlated proxy, showing that capped adaptive sampling can preserve the signal feature’s selection probability while eventually suppressing the proxy under suitable correlation conditions.

These results do not characterize LAMPS under general dependence structures, multiple correlated signal and noise groups, or more complex covariance configurations. A general theory would clarify when correlation-induced surrogate effects lead to false positives or false negatives and would provide broader guarantees for the method’s empirical robustness in correlated data.