no code implementations • 15 Mar 2022 • Zeyu Zhou, Bruce Hajek, Nakjung Choi, Anwar Walid
Particle Thompson sampling (PTS) is an approximation of Thompson sampling obtained by simply replacing the continuous distribution by a discrete distribution supported at a set of weighted static particles.
no code implementations • 1 Feb 2021 • Suryanarayana Sankagiri, Shreyas Gandlur, Bruce Hajek
We analyze the performance of the longest-chain protocol under the assumption that the communication delays are random, independent, and identically distributed.
Cryptography and Security Distributed, Parallel, and Cluster Computing
no code implementations • 21 Jan 2018 • Bruce Hajek, Suryanarayana Sankagiri
Two precursors to the message passing algorithm are analyzed: the first is a degree thresholding (DT) algorithm and the second is an algorithm based on the arrival times of the children (C) of a given vertex, where the children of a given vertex are the vertices that attached to it.
no code implementations • 21 Jan 2018 • Bruce Hajek, Suryanarayana Sankagiri
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities.
no code implementations • 20 Feb 2016 • Bruce Hajek, Yihong Wu, Jiaming Xu
We study a semidefinite programming (SDP) relaxation of the maximum likelihood estimation for exactly recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i, j$, $A_{ij} \sim P$ if $i, j$ are both in the community and $A_{ij} \sim Q$ otherwise, for two known probability distributions $P$ and $Q$.
no code implementations • 30 Oct 2015 • Bruce Hajek, Yihong Wu, Jiaming Xu
The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $\mu$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise.
no code implementations • 9 Oct 2015 • Bruce Hajek, Yihong Wu, Jiaming Xu
We show that a belief propagation algorithm achieves weak recovery if $\lambda>1/e$, beyond the Kesten-Stigum threshold by a factor of $1/e.$ The belief propagation algorithm only needs to run for $\log^\ast n+O(1) $ iterations, with the total time complexity $O(|E| \log^*n)$, where $\log^*n$ is the iterated logarithm of $n.$ Conversely, if $\lambda \leq 1/e$, no local algorithm can asymptotically outperform trivial random guessing.
no code implementations • 25 Sep 2015 • Bruce Hajek, Yihong Wu, Jiaming Xu
We study the problem of recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i, j$, $A_{ij} \sim P$ if $i, j$ both belong to the community and $A_{ij} \sim Q$ otherwise, for two known probability distributions $P$ and $Q$ depending on $n$.
no code implementations • 26 Feb 2015 • Bruce Hajek, Yihong Wu, Jiaming Xu
Extending the proof techniques, in this paper it is shown that SDP relaxations also achieve the sharp recovery threshold in the following cases: (1) Binary stochastic block model with two clusters of sizes proportional to network size but not necessarily equal; (2) Stochastic block model with a fixed number of equal-sized clusters; (3) Binary censored block model with the background graph being Erd\H{o}s-R\'enyi.
no code implementations • 16 Feb 2015 • Rui Wu, Jiaming Xu, R. Srikant, Laurent Massoulié, Marc Lelarge, Bruce Hajek
We propose an efficient algorithm that accurately estimates the individual preferences for almost all users, if there are $r \max \{m, n\}\log m \log^2 n$ pairwise comparisons per type, which is near optimal in sample complexity when $r$ only grows logarithmically with $m$ or $n$.
no code implementations • 24 Nov 2014 • Bruce Hajek, Yihong Wu, Jiaming Xu
The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across clusters.
no code implementations • 25 Jun 2014 • Bruce Hajek, Yihong Wu, Jiaming Xu
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N, q)$, where the edge probability within the community exceeds $q$ by a constant factor.
no code implementations • NeurIPS 2014 • Bruce Hajek, Sewoong Oh, Jiaming Xu
For a given assignment of items to users, we first derive an oracle lower bound of the estimation error that holds even for the more general Thurstone models.
no code implementations • 1 Oct 2013 • Jiaming Xu, Rui Wu, Kai Zhu, Bruce Hajek, R. Srikant, Lei Ying
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure.