Sequential Subspace Change-Point Detection

Xie, Liyan; Xie, Yao; Moustakides, George V.

doi:10.48550/arxiv.1811.03936

Cited by 2 publications

(3 citation statements)

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“…We propose an asynchronous Subspace-CUSUM procedure, based on jointly estimating the unknown signal waveform and the unknown relative delays. It is related to the Subspace-CUSUM procedure in our prior work [2], [10]. We extend the results therein for the asynchronous case, and develop an optimal choice of the drift parameter, which is essential for CUSUM type of procedures.…”

Section: Introductionmentioning

confidence: 72%

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Asynchronous Multi-Sensor Change-Point Detection for Seismic Tremors

Xie

Moustakides

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. We consider the sequential change-point detection for asynchronous multi-sensors, where each sensor observe a signal (due to change-point) at different times. We propose an asynchronous Subspace-CUSUM procedure based on jointly estimating the unknown signal waveform and the unknown relative delays between the sensors. Using the estimated delays, we can align signals and use the subspace to combine the multiple sensor observations. We derive the optimal drift parameter for the proposed procedure, and characterize the relationship between the expected detection delay, average run length (of false alarms), and the energy of the time-varying signal. We demonstrate the good performance of the proposed procedure using simulation and real data. We also demonstrate that the proposed procedure outperforms the well-known "one-shot procedure" in detecting weak and asynchronous signals.

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Section: Introductionmentioning

confidence: 72%

“…The well-known cumulative sum (CUSUM) test [4], [5] cumulates the log-likelihood ratio and declares an alarm whenever the cumulation exceeds a threshold. For the data model in (1), we can derive the log-likelihood ratio for each sample as the equation ( 7) in [10]:…”

Section: Background: Subspace-cusum Proceduresmentioning

confidence: 99%

Asynchronous Multi-Sensor Change-Point Detection for Seismic Tremors

Xie

Moustakides

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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“…PCA and factor models are among the most classic and extensively studied topics in statistics (Anderson, 1962;Fan et al, 2020b;Wainwright, 2019). The model considered in Section 3.5.1 has been studied by, for example, Johnstone (2001), Paul (2007), Nadler (2008), Perry et al (2018), Xie et al (2018), Wang and Fan (2017), and Fan et al (2018c) under the name of spiked covariance models, covering both the finite-sample regime and high-dimensional asymptotics. A more recent strand of work extended the theory to accommodate heteroskedastic noise and missing data (including heterogeneous missing patterns) (Lounici, 2014;Zhang et al, 2018a;Cai et al, 2019a;Zhu et al, 2019), as well as exponential family distributions (Liu et al, 2018).…”

Section: Notesmentioning

confidence: 99%

Spectral Methods for Data Science: A Statistical Perspective

Chen,

Chi,

Fan

et al. 2020

Preprint

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Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues (resp. singular values) and eigenvectors (resp. singular vectors) of some properly designed matrices constructed from data. A diverse array of applications have been found in machine learning, data science, and signal processing, including recommendation systems, community detection, ranking, structured matrix recovery, tensor completion, joint shape matching, blind deconvolution, financial investments, risk managements, econometric modeling, treatment evaluations, causal inference, amongst others. Due to their simplicity and effectiveness, spectral methods are not only used as a stand-alone estimator, but also frequently employed to initialize other more sophisticated algorithms to improve performance.While the studies of spectral methods can be traced back to classical matrix perturbation theory and methods of moments, the past decade has witnessed tremendous theoretical advances in demystifying their efficacy through the lens of statistical modeling, with the aid of nonasymptotic random matrix theory. This monograph aims to present a systematic, comprehensive, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications. In particular, our exposition gravitates around several central questions that span various applications: how to characterize the sample efficiency of spectral methods in reaching a target level of statistical accuracy, and how to assess their stability in the face of random noise, missing data, and adversarial corruptions? In addition to conventional 2 perturbation analysis, we present a systematic ∞ and 2,∞ perturbation theory for eigenspace and singular subspaces, which has only recently become available owing to a powerful "leave-one-out" analysis framework.

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Sequential Subspace Change-Point Detection

Cited by 2 publications

References 39 publications

Asynchronous Multi-Sensor Change-Point Detection for Seismic Tremors

Asynchronous Multi-Sensor Change-Point Detection for Seismic Tremors

Spectral Methods for Data Science: A Statistical Perspective

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