Non-parametric quickest change detection for large scale random matrices

Banerjee, Taposh; Firouzi, Hamed; Hero, Alfred O.

doi:10.1109/isit.2015.7282434

Cited by 6 publications

(16 citation statements)

References 20 publications

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“…With the Monte Carlo sample size M � 10 6 , we obtain the generalized p values p � 0.0431, p � 0.0022, and p � 7.02 × 10 − 4 , respectively. Given the nominal level α � 0.05, we should reject H (2) 0 and H (3) 0 , and this indicates that the inner and outer diameters do not significantly change after the second cleaning stage and the heat treatment stage.…”

Section: Case Studymentioning

confidence: 99%

“…To the best of our knowledge, there is no work on the above statistical hypothesis testing problems for detecting changes. Existing research studies on change detection in the literature [2][3][4] relate to different statistical models or focuses. Note that the distributions of the likelihood ratio statistics under the null one-sided hypotheses like (1) and ( 2) are very complicated [5].…”

Section: Introductionmentioning

confidence: 99%

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Detecting Changes under Multivariate Normal Distributions via the Generalized Inference

Wang

et al. 2021

Mathematical Problems in Engineering

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It is commonly encountered in many fields to detect whether a change occurs on a population after a special process. Based on observations for describing the population before and after the process, we formulate this problem as two statistical hypotheses testing problems within a framework of multivariate statistical analysis and then propose a generalized inference approach to solve them. The corresponding generalized p values and their calculation details are provided. The proposed method is also extended to multiple testing problems. Simulation studies show that the proposed p values have satisfactory frequentist performance. We illustrate our methods with a real application in manufacturing of bearings that are used in medical devices.

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Section: Case Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Detecting Changes under Multivariate Normal Distributions via the Generalized Inference

Wang

et al. 2021

Mathematical Problems in Engineering

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“…Results on hub discovery for these other type of hubs will be reported elsewhere. In this paper we only discuss hub discovery for hubs defined in (4).…”

Section: Problem Descriptionmentioning

confidence: 99%

“…In [4], we proposed a test for the non-parametric family of vector elliptically contoured densities, of which the Gaussian case considered here is a special case, with the objective of minimizing detection delay while avoiding false alarms. In our test in [4], we used a global summary statistic to detect the change in correlation. However, the global nature of our summary statistics in [4] does not allow for classification of where the changes occurred in the correlation matrix, i.e., correlation hub discovery.…”

Section: Problem Descriptionmentioning

confidence: 99%

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Quickest hub discovery in correlation graphs

Banerjee

Hero

2016

2016 50th Asilomar Conference on Signals, Systems and Computers

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A sequential test is proposed for detection and isolation of hubs in a correlation graph. Hubs in a correlation graph of a random vector are variables (nodes) that have a strong correlation edge. It is assumed that the random vectors are highdimensional and are multivariate Gaussian distributed. The test employs a family of novel local and global summary statistics generated from small samples of the random vectors. Delay and false alarm analysis of the test is obtained and numerical results are provided to show that the test is consistent in identifying hubs, as the false alarm rate goes to zero.

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Nonparametric change point detection for periodic time series

Guo

Modarres

2020

Can J Statistics

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We consider detection of multiple changes in the distribution of periodic and autocorrelated data with known period. To account for periodicity we transform the sequence of vector observations by arranging them in matrices and thereby producing a sequence of independently and identically distributed matrix observations. We propose methods of testing the equality of matrix distributions and present methods that can be applied to matrix observations using the E‐divisive algorithm. We show that periodicity and autocorrelation degrade existing change detection methods because they blur the changes that these procedures aim to discover. Methods that ignore the periodicity have low power to detect changes in the mean and the variance of periodic time series when the periodic effects overwhelm the true changes, while the proposed methods detect such changes with high power. We illustrate the proposed methods by detecting changes in the water quality of Lake Kasumigaura in Japan. The Canadian Journal of Statistics 48: 518–534; 2020 © 2020 Statistical Society of Canada

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Non-parametric quickest change detection for large scale random matrices

Cited by 6 publications

References 20 publications

Detecting Changes under Multivariate Normal Distributions via the Generalized Inference

Detecting Changes under Multivariate Normal Distributions via the Generalized Inference

Quickest hub discovery in correlation graphs

Nonparametric change point detection for periodic time series

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