# BELLA: Black box model Explanations by Local Linear Approximations

arXiv: https://arxiv.org/abs/2305.11311 · HTML: https://mlsanity.com/paper/2305.11311/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 68 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 30 of 31)

- [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)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Model Agnostic Supervised Local Explanations](https://mlsanity.com/paper/1807.02910/) (2018)
- [Contrastive Explanation: A Structural-Model Approach](https://mlsanity.com/paper/1811.03163/) (2018)
- [DLIME: A Deterministic Local Interpretable Model-Agnostic Explanations Approach for Computer-Aided Diagnosis Systems](https://mlsanity.com/paper/1906.10263/) (2019)
- [PMLB v1.0: An open source dataset collection for benchmarking machine learning methods](https://mlsanity.com/paper/2012.00058/) (2020)
- [Measurable Counterfactual Local Explanations for Any Classifier](https://mlsanity.com/paper/1908.03020/) (2019)
- [Interpreting Blackbox Models via Model Extraction](https://mlsanity.com/paper/1705.08504/) (2017)
- [Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead](https://mlsanity.com/paper/1811.10154/) (2018)
- [Explaining a black-box using Deep Variational Information Bottleneck Approach](https://mlsanity.com/paper/1902.06918/) (2019)
- [A Framework to Learn with Interpretation](https://mlsanity.com/paper/2010.09345/) (2020)
- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Flexible and Context-Specific AI Explainability: A Multidisciplinary Approach](https://mlsanity.com/paper/2003.07703/) (2020)
- [Feature-based Learning for Diverse and Privacy-Preserving Counterfactual Explanations](https://mlsanity.com/paper/2209.13446/) (2022)
- [AcME -- Accelerated Model-agnostic Explanations: Fast Whitening of the Machine-Learning Black Box](https://mlsanity.com/paper/2112.12635/) (2021)
- [MCCE: Monte Carlo sampling of realistic counterfactual explanations](https://mlsanity.com/paper/2111.09790/) (2021)
- [A Functional Information Perspective on Model Interpretation](https://mlsanity.com/paper/2206.05700/) (2022)

## Abstract (arXiv)

Understanding the decision-making process of black-box models has become not just a legal requirement, but also an additional way to assess their performance. However, the state of the art post-hoc explanation approaches for regression models rely on synthetic data generation, which introduces uncertainty and can hurt the reliability of the explanations. Furthermore, they tend to produce explanations that apply to only very few data points. In this paper, we present BELLA, a deterministic model-agnostic post-hoc approach for explaining the individual predictions of regression black-box models. BELLA provides explanations in the form of a linear model trained in the feature space. BELLA maximizes the size of the neighborhood to which the linear model applies so that the explanations are accurate, simple, general, and robust.