# Statistical inference using machine learning and classical techniques based on accumulated local effects (ALE)

arXiv: https://arxiv.org/abs/2310.09877 · HTML: https://mlsanity.com/paper/2310.09877/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 24 references that are in the map.
- First posted on arXiv 15 Oct 2023.

## Builds on (most cited first, 4 of 4)

- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Quantifying Model Complexity via Functional Decomposition for Better Post-Hoc Interpretability](https://mlsanity.com/paper/1904.03867/) (2019)
- [DALE: Differential Accumulated Local Effects for efficient and accurate global explanations](https://mlsanity.com/paper/2210.04542/) (2022)
- [RHALE: Robust and Heterogeneity-aware Accumulated Local Effects](https://mlsanity.com/paper/2309.11193/) (2023)

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

- [nn2poly: An R Package for Converting Neural Networks into Interpretable Polynomials](https://mlsanity.com/paper/2406.01588/) (2024)
- [Adaptive Physics-Informed Neural Networks with Multi-Category Feature Engineering for Hydrogen Sorption Prediction in Clays, Shales, and Coals](https://mlsanity.com/paper/2509.00049/) (2025)
- [Physics-Informed Neural Networks for Predicting Hydrogen Sorption in Geological Formations: Thermodynamically Constrained Deep Learning Integrating Classical Adsorption Theory](https://mlsanity.com/paper/2603.28328/) (2026)

## Abstract (arXiv)

Accumulated Local Effects (ALE) is a model-agnostic approach for global explanations of the results of black-box machine learning (ML) algorithms. There are at least three challenges with conducting statistical inference based on ALE: ensuring the reliability of ALE analyses, especially in the context of small datasets; intuitively characterizing a variable's overall effect in ML; and making robust inferences from ML data analysis. In response, we introduce innovative tools and techniques for statistical inference using ALE, establishing bootstrapped confidence intervals tailored to dataset size and introducing ALE effect size measures that intuitively indicate effects on both the outcome variable scale and a normalized scale. Furthermore, we demonstrate how to use these tools to draw reliable statistical inferences, reflecting the flexible patterns ALE adeptly highlights, with implementations available in the 'ale' package in R. This work propels the discourse on ALE and its applicability in ML and statistical analysis forward, offering practical solutions to prevailing challenges in the field.