[Paper Review] Interpretable Random Forests via Rule Extraction

Clément Bénard, Gérard Biau+2 more|arXiv (Cornell University)|Apr 29, 2020

Neural Networks and Applications36 references25 citations

TL;DR

SIRUS is a stable, interpretable regression rule extraction algorithm that derives a concise, robust list of rules from random forests by selecting frequently occurring paths. It achieves state-of-the-art predictive accuracy while ensuring high stability and simplicity, proven both empirically and theoretically via asymptotic consistency in rule selection under mild regularity conditions.

ABSTRACT

We introduce SIRUS (Stable and Interpretable RUle Set) for regression, a stable rule learning algorithm which takes the form of a short and simple list of rules. State-of-the-art learning algorithms are often referred to as "black boxes" because of the high number of operations involved in their prediction process. Despite their powerful predictivity, this lack of interpretability may be highly restrictive for applications with critical decisions at stake. On the other hand, algorithms with a simple structure-typically decision trees, rule algorithms, or sparse linear models-are well known for their instability. This undesirable feature makes the conclusions of the data analysis unreliable and turns out to be a strong operational limitation. This motivates the design of SIRUS, which combines a simple structure with a remarkable stable behavior when data is perturbed. The algorithm is based on random forests, the predictive accuracy of which is preserved. We demonstrate the efficiency of the method both empirically (through experiments) and theoretically (with the proof of its asymptotic stability). Our R/C++ software implementation sirus is available from CRAN.

Motivation & Objective

• To address the instability of traditional rule-based models and black-box algorithms in regression tasks.
• To develop a method that combines interpretability, stability, and predictive accuracy in a single framework.
• To extract a compact, stable, and interpretable rule set from random forests using frequency-based rule selection.
• To prove the asymptotic stability of the rule selection process under mild regularity assumptions.
• To provide a practical, open-source implementation for real-world applications requiring transparent decision-making.

Proposed method

• SIRUS grows a large random forest with splits restricted to q-empirical quantiles (e.g., q=10) to enhance stability.
• Each node in every tree is converted into an elementary rule defining a hyperrectangle in input space with a constant prediction.
• Rules are selected based on their empirical frequency of occurrence across the forest, using a threshold p0 to filter the most robust patterns.
• A post-processing step removes linearly dependent rules and selects a minimal, non-reduundant rule set via sparse linear aggregation.
• Theoretical analysis uses a symbolic path representation P = {(jk, rk, sk)} to define paths and derive asymptotic stability of the selected rule set.
• The method is grounded in theoretical consistency: as sample size increases, the same rule list is consistently selected across independent runs.

Experimental results

Research questions

• RQ1 Can a rule-based regression model achieve high predictive accuracy while maintaining stability under data perturbations?
• RQ2 Does restricting tree splits to quantile-based thresholds improve the stability of rule extraction from random forests?
• RQ3 Is the frequency-based selection of rules from random forests asymptotically consistent and stable?
• RQ4 How does SIRUS compare to existing rule methods like RuleFit and Node Harvest in terms of rule set size, stability, and predictive performance?
• RQ5 Can a stable, interpretable rule set be derived from tree ensembles without sacrificing predictive power?

Key findings

• SIRUS produces significantly shorter and more stable rule lists than RuleFit and Node Harvest, with rule sets typically under 10 rules, compared to 30–50 in competitors.
• Empirical results show SIRUS maintains predictive accuracy comparable to state-of-the-art methods, with unexplained variance within 10% of the best-performing method across multiple datasets.
• On the 'Machine' dataset, SIRUS achieves a mean unexplained variance of 0.27 (10-fold CV), matching the best-performing method while being more stable.
• Theoretical analysis proves that SIRUS is asymptotically stable: as sample size increases, the same rule list is consistently selected across independent runs.
• The method’s stability is attributed to quantile-based splits and the use of random forests instead of boosted ensembles, which reduces sensitivity to data perturbations.
• A R/C++ implementation named 'sirus' is available on CRAN, enabling practical deployment in industrial and scientific applications.