# SAILS: Surrogate-based Analysis of Interactions via Local Effect Smooths

arXiv: https://arxiv.org/abs/2606.09404 · HTML: https://mlsanity.com/paper/2606.09404/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 12 of 12)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Tunability: Importance of Hyperparameters of Machine Learning Algorithms](https://mlsanity.com/paper/1802.09596/) (2018)
- [A Simple and Effective Model-Based Variable Importance Measure](https://mlsanity.com/paper/1805.04755/) (2018)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [REPID: Regional Effect Plots with implicit Interaction Detection](https://mlsanity.com/paper/2202.07254/) (2022)
- [Decomposing Global Feature Effects Based on Feature Interactions](https://mlsanity.com/paper/2306.00541/) (2023)
- [RHALE: Robust and Heterogeneity-aware Accumulated Local Effects](https://mlsanity.com/paper/2309.11193/) (2023)
- [Leveraging Model-based Trees as Interpretable Surrogate Models for Model Distillation](https://mlsanity.com/paper/2310.03112/) (2023)
- [FINCH: Locally Visualizing Higher-Order Feature Interactions in Black Box Models](https://mlsanity.com/paper/2503.16445/) (2025)
- [Analyzing Error Sources in Global Feature Effect Estimation](https://mlsanity.com/paper/2603.15057/) (2026)

## Abstract (arXiv)

Feature interactions drive much of the predictive power of machine learning models, yet existing explanation methods only detect and quantify interactions without revealing their functional form, or visualize only restricted interaction types. We propose Surrogate-based Analysis of Interactions via Local Effect Smooths (SAILS), a model-agnostic framework that analyzes pairwise interactions through generalized additive model (GAM) surrogates fitted to the local effects of a black-box model. For each interval of a feature of interest, the surrogate smooth terms isolate the interaction components on derivative level, enabling (i) interaction detection through a heuristic derived from significance tests on smooth terms, (ii) interaction form categorization into linear, product-separable, and non-product-separable types, and (iii) tailored, interpretable visualizations for each interaction type. We empirically validate the framework through controlled simulations and a real-world task, showing its effectiveness for pairwise interactions, with limitations under strong feature correlations and higher-order interactions. SAILS fills a notable gap in the eXplainable AI (XAI) toolbox, going beyond detecting interactions alone to characterizing their functional form.