# Explaining Probabilistic Models with Distributional Values

arXiv: https://arxiv.org/abs/2402.09947 · HTML: https://mlsanity.com/paper/2402.09947/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 72 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [CrowS-Pairs: A Challenge Dataset for Measuring Social Biases in Masked Language Models](https://mlsanity.com/paper/2010.00133/) (2020)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Explainable Machine Learning in Deployment](https://mlsanity.com/paper/1909.06342/) (2019)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [Explaining Explanations in AI](https://mlsanity.com/paper/1811.01439/) (2018)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [What Do We Want From Explainable Artificial Intelligence (XAI)? -- A Stakeholder Perspective on XAI and a Conceptual Model Guiding Interdisciplinary XAI Research](https://mlsanity.com/paper/2102.07817/) (2021)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)

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

- [Jet Expansions of Residual Computation](https://mlsanity.com/paper/2410.06024/) (2024)
- [Explaining a probabilistic prediction on the simplex with Shapley compositions](https://mlsanity.com/paper/2408.01382/) (2024)
- [The implicated scientist: on the role of AI researchers in the development of weapons systems](https://mlsanity.com/paper/2604.18380/) (2026)

## Abstract (arXiv)

A large branch of explainable machine learning is grounded in cooperative game theory. However, research indicates that game-theoretic explanations may mislead or be hard to interpret. We argue that often there is a critical mismatch between what one wishes to explain (e.g. the output of a classifier) and what current methods such as SHAP explain (e.g. the scalar probability of a class). This paper addresses such gap for probabilistic models by generalising cooperative games and value operators. We introduce the distributional values, random variables that track changes in the model output (e.g. flipping of the predicted class) and derive their analytic expressions for games with Gaussian, Bernoulli and Categorical payoffs. We further establish several characterising properties, and show that our framework provides fine-grained and insightful explanations with case studies on vision and language models.