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Found 14 papers, 0 papers with code
Regenerative Particle Thompson Sampling
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.
The Longest-Chain Protocol Under Random Delays
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
Preferential Attachment Graphs with Planted Communities
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities.
Community Recovery in a Preferential Attachment Graph
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.
Semidefinite Programs for Exact Recovery of a Hidden Community
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 $Q$.
Submatrix localization via message passing
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.
Recovering a Hidden Community Beyond the Kesten-Stigum Threshold in $O(|E| \log^*|V|)$ Time
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.
Information Limits for Recovering a Hidden Community
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 $n$.
Achieving Exact Cluster Recovery Threshold via Semidefinite Programming: Extensions
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.
Clustering and Inference From Pairwise Comparisons
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 $n$.
Achieving Exact Cluster Recovery Threshold via Semidefinite Programming
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.
Computational Lower Bounds for Community Detection on Random Graphs
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.
Minimax-optimal Inference from Partial Rankings
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.
Jointly Clustering Rows and Columns of Binary Matrices: Algorithms and Trade-offs
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.
