2024-06-30-huang24c.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
Reconstructing the Geometry of Random Geometric Graphs (Extended Abstract)	Original Papers	Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the {\em manifold} assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in $\mathbb{R}^N$. Our work complements a large body of work on manifold learning, where the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distance	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	huang24c	0	Reconstructing the Geometry of Random Geometric Graphs (Extended Abstract)	2519	2521	2519-2521	2519	false	Huang, Han and Jiradilok, Pakawut and Mossel, Elchanan	given family Han Huang given family Pakawut Jiradilok given family Elchanan Mossel	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/huang24c/huang24c.pdf