Learning Small Decision Trees for Data of Low Rank-Width
Konrad K. Dabrowski, Eduard Eiben, Sebastian Ordyniak, Giacomo Paesani, Stefan Szeider
Abstract
We consider the NP-hard problem of finding a smallest decision tree representing a classification instance in terms of a partially defined Boolean function. Small decision trees are desirable to provide an interpretable model for the given data. We show that the problem is fixed-parameter tractable when parameterized by the rank-width of the incidence graph of the given classification instance. Our algorithm proceeds by dynamic programming using an NLC decomposition obtained from a rank-width decomposition. The key to the algorithm is a succinct representation of partial solutions. This allows us to limit the space and time requirements for each dynamic programming step in terms of the parameter.
BibTeX
@article{Dabrowski_Eiben_Ordyniak_Paesani_Szeider_2024, title={Learning Small Decision Trees for Data of Low Rank-Width}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/28916}, DOI={10.1609/aaai.v38i9.28916}, abstractNote={We consider the NP-hard problem of finding a smallest decision tree
representing a classification instance in terms of a partially defined
Boolean function. Small decision trees are desirable to provide an
interpretable model for the given data. We show that the problem is
fixed-parameter tractable when parameterized by the rank-width of the
incidence graph of the given classification instance. Our algorithm
proceeds by dynamic programming using an NLC decomposition obtained
from a rank-width decomposition. The key to the algorithm is a
succinct representation of partial solutions. This allows us to limit
the space and time requirements for each dynamic programming step in
terms of the parameter.}, number={9}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Dabrowski, Konrad K. and Eiben, Eduard and Ordyniak, Sebastian and Paesani, Giacomo and Szeider, Stefan}, year={2024}, month={Mar.}, pages={10476-10483} }