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Factor importance measures the impact of each feature on output predictionaccuracy. Many existing works focus on the model-based importance, but animportant feature in one learning algorithm may hold little significance inanother model. Hence, a factor importance measure ought to characterize thefeature's predictive potential without relying on a specific predictionalgorithm. Such algorithm-agnostic importance is termed as intrinsic importancein Williamson et al. (2023), but their estimator again requires model fitting.To bypass the modeling step, we present the equivalence between predictivenesspotential and total Sobol' indices from global sensitivity analysis, andintroduce a novel consistent estimator that can be directly estimated fromnoisy data. Integrating with forward selection and backward elimination givesrise to FIRST, Factor Importance Ranking and Selection using Total (Sobol')indices. Extensive simulations are provided to demonstrate the effectiveness ofFIRST on regression and binary classification problems, and a clear advantageover the state-of-the-art methods.

Factor Importance Ranking and Selection using Total Indices