Eiben, E, Ordyniak, S orcid.org/0000-0003-1935-651X, Paesani, G et al. (1 more author) (2023) Learning Small Decision Trees with Large Domain. In: Elkind, E, (ed.) Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence. IJCAI 2023, The 32nd International Joint Conference On Artificial Intelligence, 19-25 Aug 2023, Macau, S.A.R.. International Joint Conferences on Artificial Intelligence , pp. 3184-3192. ISBN 978-1-956792-03-4
Abstract
One favors decision trees (DTs) of the smallest size or depth to facilitate explainability and interpretability. However, learning such an optimal DT from data is well-known to be NP-hard. To overcome this complexity barrier, Ordyniak and Szeider (AAAI 21) initiated the study of optimal DT learning under the parameterized complexity perspective. They showed that solution size (i.e., number of nodes or depth of the DT) is insufficient to obtain fixed-parameter tractability (FPT). Therefore, they proposed an FPT algorithm that utilizes two auxiliary parameters: the maximum difference (as a structural property of the data set) and maximum domain size. They left it as an open question of whether bounding the maximum domain size is necessary. The main result of this paper answers this question. We present FPT algorithms for learning a smallest or lowest-depth DT from data, with the only parameters solution size and maximum difference. Thus, our algorithm is significantly more potent than the one by Szeider and Ordyniak as it can handle problem inputs with features that range over unbounded domains. We also close several gaps concerning the quality of approximation one obtains by only considering DTs based on minimum support sets.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Keywords: | Knowledge Representation and Reasoning; KRR; Computational complexity of reasoning; Machine Learning; ML; Explainable/Interpretable machine learning |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/V00252X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 31 May 2023 11:13 |
Last Modified: | 29 Nov 2024 16:55 |
Published Version: | https://doi.org/10.24963/ijcai.2023/355 |
Status: | Published |
Publisher: | International Joint Conferences on Artificial Intelligence |
Identification Number: | 10.24963/ijcai.2023/355 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:199662 |