• Corpus ID: 231603213

Optimal network online change point localisation

@article{Yu2021OptimalNO,
  title={Optimal network online change point localisation},
  author={Yi Yu and Oscar Hernan Madrid Padilla and Daren Wang and Alessandro Rinaldo},
  journal={ArXiv},
  year={2021},
  volume={abs/2101.05477}
}
We study the problem of online network change point detection. In this setting, a collection of independent Bernoulli networks is collected sequentially, and the underlying distributions change when a change point occurs. The goal is to detect the change point as quickly as possible, if it exists, subject to a constraint on the number or probability of false alarms. In this paper, on the detection delay, we establish a minimax lower bound and two upper bounds based on NP-hard algorithms and… 

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References

SHOWING 1-10 OF 35 REFERENCES
Optimal change point detection and localization in sparse dynamic networks
TLDR
This work proposes a computationally simple novel algorithm for network change point localization, called Network Binary Segmentation, which relies on weighted averages of the adjacency matrices, and devise a more sophisticated algorithm based on singular value thresholding, called Local Refinement, that delivers more accurate estimates of the change point locations.
A Note on Online Change Point Detection
Online change point detection is originated in sequential analysis, which has been thoroughly studied for more than half century. A variety of methods and optimality results have been established
Optimal Change-Point Detection and Localization
TLDR
This work establishes the energy detection threshold and shows similarly that the optimal localization error of a specific change-point becomes purely parametric, and tightly characterize optimal rates for both problems.
Sequential change-point detection based on nearest neighbors
  • Hao Chen
  • Computer Science
    The Annals of Statistics
  • 2019
We propose a new framework for the detection of change-points in online, sequential data analysis. The approach utilizes nearest neighbor information and can be applied to sequences of multivariate
Online detection of local abrupt changes in high-dimensional Gaussian graphical models
TLDR
A novel test is developed that is based on the $\ell_\infty$ norm of the normalized covariance matrix of an appropriately selected portion of incoming data and illustrates the good performance of the proposed detection procedure both in terms of computational and statistical efficiency across numerous experimental settings.
Sequential change-point detection in high-dimensional Gaussian graphical models
TLDR
This work introduces a novel scalable online algorithm for detecting an unknown number of abrupt changes in the inverse covariance matrix of sparse Gaussian graphical models with small delay and can be extended to a large class of continuous and discrete graphical models.
Sequential Graph Scanning Statistic for Change-point Detection
TLDR
This work presents two graph scanning statistics that can detect local changes in the distribution of edges in a subset of the graph and demonstrates the efficiency of the detection statistics for ambient noise imaging, using a real dataset that records real-time seismic signals around the Old Faithful Geyser in the Yellowstone National Park.
Information Bounds and Quick Detection of Parameter Changes in Stochastic Systems
  • T. Lai
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1998
TLDR
By using information-theoretic bounds and sequential hypothesis testing theory, this paper provides a new approach to optimal detection of abrupt changes in stochastic systems which leads to detection rules which have manageable computational complexity for on-line implementation and yet are nearly optimal under the different performance criteria considered.
Algorithms and Models for the Web Graph
TLDR
It is argued that the network is robust if τ < 2+ 1 δ , but fails to be robust ifτ > 2 + 1 ε−1 .
Rate-optimal graphon estimation
TLDR
This paper establishes optimal rate of convergence for graphon estimation in a H\"{o}lder class with smoothness $\alpha$, which is, to the surprise, identical to the classical nonparametric rate.
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