# iLOCO: Distribution-Free Inference for Feature Interactions

arXiv: https://arxiv.org/abs/2502.06661 · HTML: https://mlsanity.com/paper/2502.06661/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 57 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 24 of 24)

- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [Iterative Random Forests to detect predictive and stable high-order interactions](https://mlsanity.com/paper/1706.08457/) (2017)
- [Testing Conditional Independence in Supervised Learning Algorithms](https://mlsanity.com/paper/1901.09917/) (2019)
- [Explicit Feature Interaction-aware Uplift Network for Online Marketing](https://mlsanity.com/paper/2306.00315/) (2023)
- [Floodgate: inference for model-free variable importance](https://mlsanity.com/paper/2007.01283/) (2020)
- [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021)
- [Black-box tests for algorithmic stability](https://mlsanity.com/paper/2111.15546/) (2021)
- [Decorrelated Variable Importance](https://mlsanity.com/paper/2111.10853/) (2021)
- [Can I trust you more? Model-Agnostic Hierarchical Explanations](https://mlsanity.com/paper/1812.04801/) (2018)
- [Feature Selection for Huge Data via Minipatch Learning](https://mlsanity.com/paper/2010.08529/) (2020)
- [MP-Boost: Minipatch Boosting via Adaptive Feature and Observation Sampling](https://mlsanity.com/paper/2011.07218/) (2020)

## Built on by (most cited first, 3 of 3)

- [Interpretable and Explainable Surrogate Modeling for Simulations: A State-of-the-Art Survey and Perspectives on Explainable AI for Decision-Making](https://mlsanity.com/paper/2604.14240/) (2026)
- [Fair Feature Importance Scores via Feature Occlusion and Permutation](https://mlsanity.com/paper/2602.09196/) (2026)
- [Cluster LOCO: Feature Importance For Interpreting Clusters](https://mlsanity.com/paper/2606.14592/) (2026)

## Abstract (arXiv)

Feature importance measures are widely studied and are essential for understanding model behavior, guiding feature selection, and enhancing interpretability. However, many machine learning fitted models involve complex interactions between features. Existing feature importance metrics fail to capture these pairwise or higher-order effects, while existing interaction metrics often suffer from limited applicability or excessive computation; no methods exist to conduct statistical inference for feature interactions. To bridge this gap, we first propose a new model-agnostic metric, interaction Leave-One-Covariate-Out (iLOCO), for measuring the importance of pairwise feature interactions, with extensions to higher-order interactions. Next, we leverage recent advances in LOCO inference to develop distribution-free and assumption-light confidence intervals for our iLOCO metric. To address computational challenges, we also introduce an ensemble learning method for calculating the iLOCO metric and confidence intervals that we show is both computationally and statistically efficient. We validate our iLOCO metric and our confidence intervals on both synthetic and real data sets, showing that our approach outperforms existing methods and provides the first inferential approach to detecting feature interactions.