MMD-based Variable Importance for Distributional Random Forest

• URL: http://arxiv.org/abs/2310.12115v2
• Date: Wed, 14 Feb 2024 13:56:50 GMT
• Title: MMD-based Variable Importance for Distributional Random Forest
• Authors: Cl\'ement B\'enard and Jeffrey N\"af and Julie Josse
• Abstract summary: We introduce a variable importance algorithm for Distributional Random Forests (DRFs) We show that the introduced importance measure is consistent, exhibits high empirical performance on both real and simulated data, and outperforms competitors.
• Score: 5.0459880125089
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Distributional Random Forest (DRF) is a flexible forest-based method to estimate the full conditional distribution of a multivariate output of interest given input variables. In this article, we introduce a variable importance algorithm for DRFs, based on the well-established drop and relearn principle and MMD distance. While traditional importance measures only detect variables with an influence on the output mean, our algorithm detects variables impacting the output distribution more generally. We show that the introduced importance measure is consistent, exhibits high empirical performance on both real and simulated data, and outperforms competitors. In particular, our algorithm is highly efficient to select variables through recursive feature elimination, and can therefore provide small sets of variables to build accurate estimates of conditional output distributions.

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