Optimal Sparse Decision Trees (1904.12847v6)

Abstract: Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library. Our experiments highlight advantages in scalability, speed, and proof of optimality. The code is available at https://github.com/xiyanghu/OSDT.

• The paper presents a novel algorithm that finds optimal sparse decision trees by combining analytical bounds with efficient search space pruning.
• It proves significant improvements in speed and scalability, outperforming traditional methods like CART and BinOCT on real-world datasets.
• The approach leverages specialized data structures and bit-vector operations to reduce redundancy and ensure transparent, interpretable models.

Optimal Sparse Decision Trees: An Overview

The paper, "Optimal Sparse Decision Trees" by Hu, Rudin, and Seltzer, addresses a longstanding issue within interpretable machine learning: the challenge of constructing decision trees that are not only interpretable but also provably optimal. Traditional decision tree algorithms such as CART and C4.5 are frequently used due to their transparency, yet they suffer from inherent limitations in terms of optimality. These algorithms employ greedy strategies that often result in suboptimal models, a problem rooted both in theoretical difficulty and practical inefficacies in decision tree optimization.

The authors contribute to this field by introducing an innovative method for constructing optimal sparse decision trees specifically for binary variables. Unlike previous efforts that relied on general-purpose optimization toolboxes or made strong simplifying assumptions, their proposed algorithm combines analytical bounds with advanced systems techniques to effectively prune the search space, enabling the discovery of optimal trees within a pragmatic timeframe. The approach leverages rich data structures and a custom bit-vector library to enhance computational efficiency.

Key Contributions

1. Practical Algorithm for Optimal Decision Trees: The development of a novel algorithm that finds optimal decision trees by integrating analytical bounds for search space pruning within a computationally feasible framework.
2. Scalability and Efficiency: Through the co-design of theoretical and systems-level solutions, the algorithm demonstrates significant advantages in speed, scalability, and the ability to prove optimality, even when applied to real-world datasets with substantial size and feature complexity.
3. Data Structure Enhancements: The incorporation of specialized data structures and bit-vector operations facilitates rapid evaluations and computations, making the algorithm applicable to substantial datasets without prohibitive computational costs.
4. Comparative Performance: This work provides empirical evidence that many existing methodologies fall short of their claimed optimality. The proposed approach not only rectifies this for specific benchmarks but noticeably outperforms methods such as BinOCT, particularly where unnecessary tree complexity could arise.
5. Algorithmic Innovations: Introduction of bounds that ensure only necessary and sufficient tree evaluations occur, effectively reducing computational redundancy and ensuring that only optimal model constructions are pursued.

Implications

Theoretical Impact: The authors' work provides a framework that enhances our understanding of decision tree optimality by offering a new lens through which these models can be analysed and improved. It facilitates a theoretical benchmark against which interpretable models can be developed, reinforcing the standards of rigour that are crucial as the field continues to evolve.

Practical Applications: In high-stakes domains such as healthcare, finance, and criminal justice, interpretable models can significantly influence decision-making and fairness. The ability to ensure optimal model construction empowers stakeholders to replace opaque, black-box models with those that can justify decisions transparently, promoting both fairness and trust.

Future Directions: The paper paves the way for future exploration into more extensive datasets, potentially involving multiclass problems or continuous features. Additionally, integrating parallel processing techniques could further scale the algorithm's applicability, fostering an era where optimal and interpretable models are no longer mutually exclusive.

In summary, the paper by Hu, Rudin, and Seltzer makes notable advancements in decision tree optimization. By addressing both theoretical and practical barriers, their contributions represent a substantial step forward in the quest for interpretable, optimal machine learning models. This work sets a new standard for future research in interpretable AI and offers strong computational improvements that can be directly applied to pressing societal challenges.