A general framework for inference on algorithm-agnostic variable importance

• URL: http://arxiv.org/abs/2004.03683v2
• Date: Mon, 13 Sep 2021 23:37:30 GMT
• Title: A general framework for inference on algorithm-agnostic variable importance
• Authors: Brian D. Williamson, Peter B. Gilbert, Noah R. Simon, Marco Carone
• Abstract summary: We propose a framework for non inference on interpretable algorithm-agnostic variable importance. We show that our proposal has good operating characteristics, and we illustrate it with data from a study of an antibody against HIV-1 infection.
• Score: 3.441021278275805
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response -- in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may provide a misleading reflection of the intrinsic value of these features. To address this limitation, we propose a general framework for nonparametric inference on interpretable algorithm-agnostic variable importance. We define variable importance as a population-level contrast between the oracle predictiveness of all available features versus all features except those under consideration. We propose a nonparametric efficient estimation procedure that allows the construction of valid confidence intervals, even when machine learning techniques are used. We also outline a valid strategy for testing the null importance hypothesis. Through simulations, we show that our proposal has good operating characteristics, and we illustrate its use with data from a study of an antibody against HIV-1 infection.

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