# DALE: Differential Accumulated Local Effects for efficient and accurate global explanations

arXiv: https://arxiv.org/abs/2210.04542 · HTML: https://mlsanity.com/paper/2210.04542/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 10 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Metrics for Explainable AI: Challenges and Prospects](https://mlsanity.com/paper/1812.04608/) (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)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [Quantifying Model Complexity via Functional Decomposition for Better Post-Hoc Interpretability](https://mlsanity.com/paper/1904.03867/) (2019)
- [Fooling Partial Dependence via Data Poisoning](https://mlsanity.com/paper/2105.12837/) (2021)

## Built on by (most cited first, 11 of 11)

- [RHALE: Robust and Heterogeneity-aware Accumulated Local Effects](https://mlsanity.com/paper/2309.11193/) (2023)
- [Interpretable machine learning for time-to-event prediction in medicine and healthcare](https://mlsanity.com/paper/2303.09817/) (2023)
- [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)
- [Understanding User Preferences in Explainable Artificial Intelligence: A Survey and a Mapping Function Proposal](https://mlsanity.com/paper/2302.03180/) (2023)
- [Effector: A Python package for regional explanations](https://mlsanity.com/paper/2404.02629/) (2024)
- [Accumulated Aggregated D-Optimal Designs for Estimating Main Effects in Black-Box Models](https://mlsanity.com/paper/2510.08465/) (2025)
- [Analyzing Error Sources in Global Feature Effect Estimation](https://mlsanity.com/paper/2603.15057/) (2026)
- [Interpretability-by-Design with Accurate Locally Additive Models and Conditional Feature Effects](https://mlsanity.com/paper/2602.16503/) (2026)
- [Beyond Tracking or Shortcut: Composition-Bounded Predictive States in Poker Autoregressive Models](https://mlsanity.com/paper/2607.19369/) (2026)

## Abstract (arXiv)

Accumulated Local Effect (ALE) is a method for accurately estimating feature effects, overcoming fundamental failure modes of previously-existed methods, such as Partial Dependence Plots. However, ALE's approximation, i.e. the method for estimating ALE from the limited samples of the training set, faces two weaknesses. First, it does not scale well in cases where the input has high dimensionality, and, second, it is vulnerable to out-of-distribution (OOD) sampling when the training set is relatively small. In this paper, we propose a novel ALE approximation, called Differential Accumulated Local Effects (DALE), which can be used in cases where the ML model is differentiable and an auto-differentiable framework is accessible. Our proposal has significant computational advantages, making feature effect estimation applicable to high-dimensional Machine Learning scenarios with near-zero computational overhead. Furthermore, DALE does not create artificial points for calculating the feature effect, resolving misleading estimations due to OOD sampling. Finally, we formally prove that, under some hypotheses, DALE is an unbiased estimator of ALE and we present a method for quantifying the standard error of the explanation. Experiments using both synthetic and real datasets demonstrate the value of the proposed approach.