Spotlight Poster

Private estimation algorithms for stochastic block models and mixture models

Hongjie Chen · Vincent Cohen-Addad · Tommaso d’Orsi · Alessandro Epasto · Jacob Imola · David Steurer · Stefan Tiegel

Great Hall & Hall B1+B2 (level 1) #1626
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Wed 13 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms.To illustrate our techniques, we consider two problems: recovery of stochastic block models and learning mixtures of spherical Gaussians.For the former, we present the first efficient $(\epsilon, \delta)$-differentially private algorithm for both weak recovery and exact recovery. Previously known algorithms achieving comparable guarantees required quasi-polynomial time. For the latter, we design an $(\epsilon, \delta)$-differentially private algorithm that recovers the centers of the $k$-mixture when the minimum separation is at least $O(k^{1/t}\sqrt{t})$. For all choices of $t$, this algorithm requires sample complexity $n\geq k^{O(1)}d^{O(t)}$ and time complexity $(nd)^{O(t)}$. Prior work required either an additional additive $\Omega(\sqrt{\log n})$ term in the minimum separation or an explicit upper bound on the Euclidean norm of the centers.

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