2023-07-02-kalinke23a.md

abstract	openreview	title	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
Kernel techniques are among the most popular and powerful approaches of data science. Among the key features that make kernels ubiquitous are (i) the number of domains they have been designed for, (ii) the Hilbert structure of the function class associated to kernels facilitating their statistical analysis, and (iii) their ability to represent probability distributions without loss of information. These properties give rise to the immense success of Hilbert-Schmidt independence criterion (HSIC) which is able to capture joint independence of random variables under mild conditions, and permits closed-form estimators with quadratic computational complexity (w.r.t. the sample size). In order to alleviate the quadratic computational bottleneck in large-scale applications, multiple HSIC approximations have been proposed, however these estimators are restricted to $M=2$ random variables, do not extend naturally to the $M\ge 2$ case, and lack theoretical guarantees. In this work, we propose an alternative Nyström-based HSIC estimator which handles the $M\ge 2$ case, prove its consistency, and demonstrate its applicability in multiple contexts, including synthetic examples, dependency testing of media annotations, and causal discovery.	UE8MtVeVS3	Nyström $M$-Hilbert-Schmidt independence criterion	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	kalinke23a	0	Nyström $M$-{H}ilbert-{S}chmidt independence criterion	1005	1015	1005-1015	1005	false	Kalinke, Florian and Szab\'{o}, Zolt\'{a}n	given family Florian Kalinke given family Zoltán Szabó	2023-07-02		Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence	216	inproceedings	date-parts 2023 7 2	https://proceedings.mlr.press/v216/kalinke23a/kalinke23a.pdf	label link Supplementary PDF https://proceedings.mlr.press/v216/kalinke23a/kalinke23a-supp.pdf