Optimal Sparse Regression Trees

• URL: http://arxiv.org/abs/2211.14980v3
• Date: Mon, 10 Apr 2023 01:21:11 GMT
• Title: Optimal Sparse Regression Trees
• Authors: Rui Zhang, Rui Xin, Margo Seltzer, Cynthia Rudin
• Abstract summary: This work proposes a dynamic-programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm in 1-dimension over the set of labels.
• Score: 24.03491277969824
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees, there has been little effort towards full provable optimization, mainly due to the computational hardness of the problem. This work proposes a dynamic-programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm in 1-dimension over the set of labels. We are often able to find optimal sparse trees in seconds, even for challenging datasets that involve large numbers of samples and highly-correlated features.

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