# FIRE: An Optimization Approach for Fast Interpretable Rule Extraction

arXiv: https://arxiv.org/abs/2306.07432 · HTML: https://mlsanity.com/paper/2306.07432/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 12 Jun 2023.

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

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than Random Selection](https://mlsanity.com/paper/1506.00552/) (2015)
- [Generalized Linear Rule Models](https://mlsanity.com/paper/1906.01761/) (2019)
- [L0Learn: A Scalable Package for Sparse Learning using L0 Regularization](https://mlsanity.com/paper/2202.04820/) (2022)
- [Efficient Greedy Coordinate Descent for Composite Problems](https://mlsanity.com/paper/1810.06999/) (2018)
- [Correlated Feature Selection with Extended Exclusive Group Lasso](https://mlsanity.com/paper/2002.12460/) (2020)

## Built on by (most cited first, 5 of 5)

- [Learning Interpretable Rules for Scalable Data Representation and Classification](https://mlsanity.com/paper/2310.14336/) (2023)
- [A Unified Approach to Extract Interpretable Rules from Tree Ensembles via Integer Programming](https://mlsanity.com/paper/2407.00843/) (2024)
- [MOSS: Multi-Objective Optimization for Stable Rule Sets](https://mlsanity.com/paper/2506.08030/) (2025)
- [Why Global LLM Leaderboards Are Misleading: Small Portfolios for Heterogeneous Supervised ML](https://mlsanity.com/paper/2605.06656/) (2026)
- [Minimax Rates and Spectral Distillation for Tree Ensembles](https://mlsanity.com/paper/2605.11841/) (2026)

## Abstract (arXiv)

We present FIRE, Fast Interpretable Rule Extraction, an optimization-based framework to extract a small but useful collection of decision rules from tree ensembles. FIRE selects sparse representative subsets of rules from tree ensembles, that are easy for a practitioner to examine. To further enhance the interpretability of the extracted model, FIRE encourages fusing rules during selection, so that many of the selected decision rules share common antecedents. The optimization framework utilizes a fusion regularization penalty to accomplish this, along with a non-convex sparsity-inducing penalty to aggressively select rules. Optimization problems in FIRE pose a challenge to off-the-shelf solvers due to problem scale and the non-convexity of the penalties. To address this, making use of problem-structure, we develop a specialized solver based on block coordinate descent principles; our solver performs up to 40x faster than existing solvers. We show in our experiments that FIRE outperforms state-of-the-art rule ensemble algorithms at building sparse rule sets, and can deliver more interpretable models compared to existing methods.