Multicollinearity-agnostic feature screening for non-Euclidean responses: a factor adjusted approach
Abstract
In high-dimensional settings, multicollinearity is a pervasive issue that can substantially impair the performance of feature screening methods based on marginal Fr\'echet regression. Feature screening for non-Euclidean responses becomes unreliable when ultrahigh-dimensional predictors suffer from multicollinearity, because feature-specific signals may be masked by shared latent factors. To mitigate this effect, we propose a Factor adjusted Fr\'echet sure independence screening procedure. The method first recovers latent common factors from the predictors and then evaluates each feature by the incremental Fr\'echet coefficient of determination contributed by its idiosyncratic component beyond the common factors. Under regularity conditions, we establish uniform approximation rates for the feasible screening utilities and prove the sure screening and sure ranking properties. Extensive numerical experiments provide compelling empirical support for the validity and effectiveness of our approach, particularly in scenarios with highly correlated covariates. We further illustrate the practical performance of our method through two representative non-Euclidean datasets: the ADNI dataset and the mortality dataset, both with distribution-valued responses.