基于SAT的显式路径最优决策树编码
SAT-based Encodings for Optimal Decision Trees with Explicit Paths
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中文总结 AI 辅助
本文提出一种显式建模路径的SAT编码方法，以精确控制决策树深度与规模，通过先最小化深度再最小化节点数的策略，在求解更大规模实例上优于现有工具。
中文摘要 AI 辅助
决策树在机器学习与知识表示领域均扮演重要角色。由于其即时可解释性，决策树颇具吸引力。本着奥卡姆剃刀原则及可解释性精神，计算最小规模的树是理想之选。然而，这已被证明是一项具有挑战性的任务，实践中通常采用贪心方法学习决策树。尽管如此，近期工作表明，借助SAT求解器，可以针对现实世界基准计算出最优规模的树。本文提出一种新颖的基于SAT的编码方法，显式地对树中的路径进行建模，从而能够同时控制树的深度与规模。在单个SAT调用的层面上，我们研究了将搜索空间划分为树拓扑结构的方法。我们的工具优于现有实现。此外，实验结果表明，先最小化深度再最小化节点数，能够求解更大规模的实例集。
英文摘要
Decision trees play an important role both in Machine Learning and Knowledge Representation. They are attractive due to their immediate interpretability. In the spirit of Occam's razor, and interpretability, it is desirable to calculate the smallest tree. This, however, has proven to be a challenging task and greedy approaches are typically used to learn trees in practice. Nevertheless, recent work showed that by the use of SAT solvers one may calculate the optimal size tree for real-world benchmarks. This paper proposes a novel SAT-based encoding that explicitly models paths in the tree, which enables us to control the tree's depth as well as size. At the level of individual SAT calls, we investigate splitting the search space into tree topologies. Our tool outperforms the existing implementation. But also, the experimental results show that minimizing the depth first and then minimizing the number of nodes enables solving a larger set of instances.
发表机构
- INESC-ID/IST, U. de Lisboa, Portugal（里斯本大学）
- Czech Technical University in Prague, Czech Republic（布拉格捷克理工大学）
机构由 AI 辅助整理，请以论文原文为准。
