2019-06-25-fei19a.md

abstract	section	title	layout	series	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	publisher	container-title	volume	genre	issued	pdf	extras
We study the statistical performance of the semidefinite programming (SDP) relaxation approach for clustering under the binary symmetric Stochastic Block Model (SBM). We show that the SDP achieves an error rate of the form $\exp\left[-(1-o(1))\frac{n I}{2}\right]$, where $I$ is an appropriate information-theoretic measure of the signal-to-noise ratio. This bound matches the minimax lower bound on the optimal Bayes error rate for this problem, and improves upon existing results that are sub-optimal by a multiplicative constant in the exponent. As a corollary, our result implies that SDP achieves the optimal exact recovery threshold with the correct leading constant. We further show that this error rate of SDP is robust; that is, it remains unchanged under the so-called semirandom model where the graph is modified by a monotone adversary, as well as under the setting with heterogeneous edge probabilities. Our proof is based on a novel primal-dual analysis of the SDP.	contributed	Achieving the Bayes Error Rate in Stochastic Block Model by SDP, Robustly	inproceedings	Proceedings of Machine Learning Research	fei19a	0	Achieving the Bayes Error Rate in Stochastic Block Model by SDP, Robustly	1235	1269	1235-1269	1235	false	Fei, Yingjie and Chen, Yudong	given family Yingjie Fei given family Yudong Chen	2019-06-25		PMLR	Proceedings of the Thirty-Second Conference on Learning Theory	99	inproceedings	date-parts 2019 6 25	http://proceedings.mlr.press/v99/fei19a/fei19a.pdf