SORTeD Rashomon Sets of Sparse Decision Trees: Anytime Enumeration

2025-11-05

AI Summary

This paper addresses the inefficiency of enumerating the Rashomon set—i.e., the collection of sparse decision trees with comparable predictive performance but structurally distinct topologies. We propose SORTD, the first framework enabling *ordered* (by objective value) and *anytime* enumeration of decision trees within the Rashomon set. Its core innovations include: (i) a decomposable, totally ordered objective function enabling aggressive pruning, and (ii) an integrated dynamic search and backtracking mechanism supporting post-hoc multi-objective evaluation over partially ordered, separable criteria (e.g., simplicity, fairness). Experiments demonstrate that SORTD achieves up to two orders-of-magnitude speedup over state-of-the-art methods while preserving solution quality. This substantial computational gain significantly enhances the practical utility and tractability of the Rashomon set for real-world applications—including feature importance analysis, interpretability enhancement, and user-preference-driven model selection.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Sparse decision tree learning provides accurate and interpretable predictive models that are ideal for high-stakes applications by finding the single most accurate tree within a (soft) size limit. Rather than relying on a single"best"tree, Rashomon sets-trees with similar performance but varying structures-can be used to enhance variable importance analysis, enrich explanations, and enable users to choose simpler trees or those that satisfy stakeholder preferences (e.g., fairness) without hard-coding such criteria into the objective function. However, because finding the optimal tree is NP-hard, enumerating the Rashomon set is inherently challenging. Therefore, we introduce SORTD, a novel framework that improves scalability and enumerates trees in the Rashomon set in order of the objective value, thus offering anytime behavior. Our experiments show that SORTD reduces runtime by up to two orders of magnitude compared with the state of the art. Moreover, SORTD can compute Rashomon sets for any separable and totally ordered objective and supports post-evaluating the set using other separable (and partially ordered) objectives. Together, these advances make exploring Rashomon sets more practical in real-world applications.

Problem

• Enumerating Rashomon sets of sparse decision trees efficiently
• Overcoming NP-hard complexity in finding optimal decision trees
• Supporting multiple objectives for post-evaluation of tree sets

Innovation

• Enumerates Rashomon sets of sparse decision trees
• Introduces SORTD framework for anytime enumeration
• Improves scalability by reducing runtime significantly