# RHALE: Robust and Heterogeneity-aware Accumulated Local Effects

arXiv: https://arxiv.org/abs/2309.11193 · HTML: https://mlsanity.com/paper/2309.11193/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 24 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 16 of 16)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Interpretable Machine Learning -- A Brief History, State-of-the-Art and Challenges](https://mlsanity.com/paper/2010.09337/) (2020)
- [General Pitfalls of Model-Agnostic Interpretation Methods for Machine Learning Models](https://mlsanity.com/paper/2007.04131/) (2020)
- [Visualizing the Feature Importance for Black Box Models](https://mlsanity.com/paper/1804.06620/) (2018)
- [A Simple and Effective Model-Based Variable Importance Measure](https://mlsanity.com/paper/1805.04755/) (2018)
- [Model-agnostic Feature Importance and Effects with Dependent Features -- A Conditional Subgroup Approach](https://mlsanity.com/paper/2006.04628/) (2020)
- [Relating the Partial Dependence Plot and Permutation Feature Importance to the Data Generating Process](https://mlsanity.com/paper/2109.01433/) (2021)
- [Scientific Inference With Interpretable Machine Learning: Analyzing Models to Learn About Real-World Phenomena](https://mlsanity.com/paper/2206.05487/) (2022)
- [REPID: Regional Effect Plots with implicit Interaction Detection](https://mlsanity.com/paper/2202.07254/) (2022)
- [Fooling Partial Dependence via Data Poisoning](https://mlsanity.com/paper/2105.12837/) (2021)
- [VINE: Visualizing Statistical Interactions in Black Box Models](https://mlsanity.com/paper/1904.00561/) (2019)
- [DALE: Differential Accumulated Local Effects for efficient and accurate global explanations](https://mlsanity.com/paper/2210.04542/) (2022)

## Built on by (most cited first, 8 of 8)

- [Regionally Additive Models: Explainable-by-design models minimizing feature interactions](https://mlsanity.com/paper/2309.12215/) (2023)
- [Statistical inference using machine learning and classical techniques based on accumulated local effects (ALE)](https://mlsanity.com/paper/2310.09877/) (2023)
- [On the Robustness of Global Feature Effect Explanations](https://mlsanity.com/paper/2406.09069/) (2024)
- [Effector: A Python package for regional explanations](https://mlsanity.com/paper/2404.02629/) (2024)
- [Analyzing Error Sources in Global Feature Effect Estimation](https://mlsanity.com/paper/2603.15057/) (2026)
- [Neural Additive Experts: Context-Gated Experts for Controllable Model Additivity](https://mlsanity.com/paper/2602.10585/) (2026)
- [Interpretability-by-Design with Accurate Locally Additive Models and Conditional Feature Effects](https://mlsanity.com/paper/2602.16503/) (2026)
- [SAILS: Surrogate-based Analysis of Interactions via Local Effect Smooths](https://mlsanity.com/paper/2606.09404/) (2026)

## Abstract (arXiv)

Accumulated Local Effects (ALE) is a widely-used explainability method for isolating the average effect of a feature on the output, because it handles cases with correlated features well. However, it has two limitations. First, it does not quantify the deviation of instance-level (local) effects from the average (global) effect, known as heterogeneity. Second, for estimating the average effect, it partitions the feature domain into user-defined, fixed-sized bins, where different bin sizes may lead to inconsistent ALE estimations. To address these limitations, we propose Robust and Heterogeneity-aware ALE (RHALE). RHALE quantifies the heterogeneity by considering the standard deviation of the local effects and automatically determines an optimal variable-size bin-splitting. In this paper, we prove that to achieve an unbiased approximation of the standard deviation of local effects within each bin, bin splitting must follow a set of sufficient conditions. Based on these conditions, we propose an algorithm that automatically determines the optimal partitioning, balancing the estimation bias and variance. Through evaluations on synthetic and real datasets, we demonstrate the superiority of RHALE compared to other methods, including the advantages of automatic bin splitting, especially in cases with correlated features.