# CON-FOLD -- Explainable Machine Learning with Confidence

arXiv: https://arxiv.org/abs/2408.07854 · HTML: https://mlsanity.com/paper/2408.07854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 7 of 7)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [The ILASP system for Inductive Learning of Answer Set Programs](https://mlsanity.com/paper/2005.00904/) (2020)
- [FOLD-SE: An Efficient Rule-based Machine Learning Algorithm with Scalable Explainability](https://mlsanity.com/paper/2208.07912/) (2022)
- [A New Algorithm to Automate Inductive Learning of Default Theories](https://mlsanity.com/paper/1707.02693/) (2017)
- [FOLD-R++: A Scalable Toolset for Automated Inductive Learning of Default Theories from Mixed Data](https://mlsanity.com/paper/2110.07843/) (2021)
- [FOLD-RM: A Scalable, Efficient, and Explainable Inductive Learning Algorithm for Multi-Category Classification of Mixed Data](https://mlsanity.com/paper/2202.06913/) (2022)
- [Bottom-Up Stratified Probabilistic Logic Programming with Fusemate](https://mlsanity.com/paper/2308.15862/) (2023)

## Built on by (most cited first, 2 of 2)

- [Overview of AI Grading of Physics Olympiad Exams](https://mlsanity.com/paper/2505.02121/) (2025)
- [Identifying Good Rules for Efficient SAT Encodings of Single-Constant Multiplication Using Machine Learning](https://mlsanity.com/paper/2607.21188/) (2026)

## Abstract (arXiv)

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns probability-based confidence scores to rules learned for a classification task. This allows users to know how confident they should be in a prediction made by the model. We present a confidence-based pruning algorithm that uses the unique structure of FOLD-RM rules to efficiently prune rules and prevent overfitting. Furthermore, CON-FOLD enables the user to provide pre-existing knowledge in the form of logic program rules that are either (fixed) background knowledge or (modifiable) initial rule candidates. The paper describes our method in detail and reports on practical experiments. We demonstrate the performance of the algorithm on benchmark datasets from the UCI Machine Learning Repository. For that, we introduce a new metric, Inverse Brier Score, to evaluate the accuracy of the produced confidence scores. Finally we apply this extension to a real world example that requires explainability: marking of student responses to a short answer question from the Australian Physics Olympiad.