2024-06-30-bressan24b.md

title	section	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Efficient Algorithms for Learning Monophonic Halfspaces in Graphs	Original Papers	We study the problem of learning a binary classifier on the vertices of a graph. In particular, we consider classifiers given by \emph{monophonic halfspaces}, partitions of the vertices that are convex in a certain abstract sense. Monophonic halfspaces, and related notions such as geodesic halfspaces, have recently attracted interest, and several connections have been drawn between their properties (e.g., their VC dimension) and the structure of the underlying graph $G$. We prove several novel results for learning monophonic halfspaces in the supervised, online, and active settings. Our main result is that a monophonic halfspace can be learned with near-optimal passive sample complexity in time polynomial in $n=|V(G)|$. This requires us to devise a polynomial-time algorithm for consistent hypothesis checking, based on several structural insights on monophonic halfspaces and on a reduction to 2-satisfiability. We prove similar results for the online and active settings. We also show that the concept class can be enumerated with delay $\mathrm{poly}(n)$, and that empirical risk minimization can be performed in time $2^{\omega(G)}\mathrm{poly}(n)$ where $\omega(G)$ is the clique number of $G$. These results answer open questions from the literature (González et al. 2020), and show a contrast with geodesic halfspaces, for which some of the said problems are NP-hard (Seiffarth et al., 2023).	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	bressan24b	0	Efficient Algorithms for Learning Monophonic Halfspaces in Graphs	669	696	669-696	669	false	Bressan, Marco and Esposito, Emmanuel and Thiessen, Maximilian	given family Marco Bressan given family Emmanuel Esposito given family Maximilian Thiessen	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/bressan24b/bressan24b.pdf