# Grouped variable importance with random forests and application to multiple functional data analysis

arXiv: https://arxiv.org/abs/1411.4170 · HTML: https://mlsanity.com/paper/1411.4170/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2014.

## Built on by (most cited first, 16 of 16)

- [Towards a Science of Human-AI Decision Making: A Survey of Empirical Studies](https://mlsanity.com/paper/2112.11471/) (2021)
- [Grouped Feature Importance and Combined Features Effect Plot](https://mlsanity.com/paper/2104.11688/) (2021)
- [MDA for random forests: inconsistency, and a practical solution via the Sobol-MDA](https://mlsanity.com/paper/2102.13347/) (2021)
- [Incremental Permutation Feature Importance (iPFI): Towards Online Explanations on Data Streams](https://mlsanity.com/paper/2209.01939/) (2022)
- [Feature Importance Explanations for Temporal Black-Box Models](https://mlsanity.com/paper/2102.11934/) (2021)
- [Supervised Learning via Ensembles of Diverse Functional Representations: the Functional Voting Classifier](https://mlsanity.com/paper/2403.15778/) (2024)
- [Random survival forests with multivariate longitudinal endogenous covariates](https://mlsanity.com/paper/2208.05801/) (2022)
- [Variable Importance in High-Dimensional Settings Requires Grouping](https://mlsanity.com/paper/2312.10858/) (2023)
- [Triplot: model agnostic measures and visualisations for variable importance in predictive models that take into account the hierarchical correlation structure](https://mlsanity.com/paper/2104.03403/) (2021)
- [Randomized Spline Trees for Functional Data Classification: Theory and Application to Environmental Time Series](https://mlsanity.com/paper/2409.07879/) (2024)
- [The Most Important Features in Generalized Additive Models Might Be Groups of Features](https://mlsanity.com/paper/2506.19937/) (2025)
- [Augmented Functional Random Forests: Classifier Construction and Unbiased Functional Principal Components Importance through Ad-Hoc Conditional Permutations](https://mlsanity.com/paper/2408.13179/) (2024)
- [Enriched Functional Tree-Based Classifiers: A Novel Approach Leveraging Derivatives and Geometric Features](https://mlsanity.com/paper/2409.17804/) (2024)
- [L1-Regularized Functional Support Vector Machine](https://mlsanity.com/paper/2508.05567/) (2025)
- [Multimodality Stacking with Blockwise missing values and application to the PIONeeR biomarkers study for prediction of resistance to immunotherapy](https://mlsanity.com/paper/2605.25050/) (2026)
- [Benchmarking ConvLSTM for One-Day-Ahead IMDAA Rainfall-Field Prediction across Four Indian Cities](https://mlsanity.com/paper/2607.26581/) (2026)

## Abstract (arXiv)

The selection of grouped variables using the random forest algorithm is considered. First a new importance measure adapted for groups of variables is proposed. Theoretical insights into this criterion are given for additive regression models. Second, an original method for selecting functional variables based on the grouped variable importance measure is developed. Using a wavelet basis, it is proposed to regroup all of the wavelet coefficients for a given functional variable and use a wrapper selection algorithm with these groups. Various other groupings which take advantage of the frequency and time localization of the wavelet basis are proposed. An extensive simulation study is performed to illustrate the use of the grouped importance measure in this context. The method is applied to a real life problem coming from aviation safety.