# Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delay

arXiv: https://arxiv.org/abs/2008.05803 · HTML: https://mlsanity.com/paper/2008.05803/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2020.

## Built on by (most cited first, 30 of 57)

- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [On Explaining Random Forests with SAT](https://mlsanity.com/paper/2105.10278/) (2021)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [On Tackling Explanation Redundancy in Decision Trees](https://mlsanity.com/paper/2205.09971/) (2022)
- [On the Computational Intelligibility of Boolean Classifiers](https://mlsanity.com/paper/2104.06172/) (2021)
- [SAT-Based Rigorous Explanations for Decision Lists](https://mlsanity.com/paper/2105.06782/) (2021)
- [Explanations for Monotonic Classifiers](https://mlsanity.com/paper/2106.00154/) (2021)
- [On Efficiently Explaining Graph-Based Classifiers](https://mlsanity.com/paper/2106.01350/) (2021)
- [On Computing Probabilistic Explanations for Decision Trees](https://mlsanity.com/paper/2207.12213/) (2022)
- [Trading Complexity for Sparsity in Random Forest Explanations](https://mlsanity.com/paper/2108.05276/) (2021)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [VeriX: Towards Verified Explainability of Deep Neural Networks](https://mlsanity.com/paper/2212.01051/) (2022)
- [Foundations of Symbolic Languages for Model Interpretability](https://mlsanity.com/paper/2110.02376/) (2021)
- [Probabilistic Sufficient Explanations](https://mlsanity.com/paper/2105.10118/) (2021)
- [Formally Explaining Neural Networks within Reactive Systems](https://mlsanity.com/paper/2308.00143/) (2023)
- [Eliminating The Impossible, Whatever Remains Must Be True](https://mlsanity.com/paper/2206.09551/) (2022)
- [Feature Necessity & Relevancy in ML Classifier Explanations](https://mlsanity.com/paper/2210.15675/) (2022)
- [Logic for Explainable AI](https://mlsanity.com/paper/2305.05172/) (2023)
- [Local vs. Global Interpretability: A Computational Complexity Perspective](https://mlsanity.com/paper/2406.02981/) (2024)
- [On Computing Probabilistic Abductive Explanations](https://mlsanity.com/paper/2212.05990/) (2022)
- [Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations](https://mlsanity.com/paper/2506.08505/) (2025)
- [Disproving XAI Myths with Formal Methods -- Initial Results](https://mlsanity.com/paper/2306.01744/) (2023)
- [Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasons](https://mlsanity.com/paper/2502.03391/) (2025)
- [On Formal Feature Attribution and Its Approximation](https://mlsanity.com/paper/2307.03380/) (2023)
- [Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretation](https://mlsanity.com/paper/2408.03915/) (2024)
- [Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective](https://mlsanity.com/paper/2502.02719/) (2025)
- [Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees](https://mlsanity.com/paper/2602.16823/) (2026)
- [Axiomatic Aggregations of Abductive Explanations](https://mlsanity.com/paper/2310.03131/) (2023)
- [Explaining k-Nearest Neighbors: Abductive and Counterfactual Explanations](https://mlsanity.com/paper/2501.06078/) (2025)
- [Anytime Approximate Formal Feature Attribution](https://mlsanity.com/paper/2312.06973/) (2023)

## Abstract (arXiv)

Recent work proposed the computation of so-called PI-explanations of Naive Bayes Classifiers (NBCs). PI-explanations are subset-minimal sets of feature-value pairs that are sufficient for the prediction, and have been computed with state-of-the-art exact algorithms that are worst-case exponential in time and space. In contrast, we show that the computation of one PI-explanation for an NBC can be achieved in log-linear time, and that the same result also applies to the more general class of linear classifiers. Furthermore, we show that the enumeration of PI-explanations can be obtained with polynomial delay. Experimental results demonstrate the performance gains of the new algorithms when compared with earlier work. The experimental results also investigate ways to measure the quality of heuristic explanations