Optimal sequential detection in multi-stream data

Chan, Hock Peng

doi:10.1214/17-aos1546

Cited by 46 publications

(46 citation statements)

References 16 publications

(29 reference statements)

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“…Second, we study a much larger space of possible changes, including changes in only one parameter at a time. Such change scenarios where only a few of the dimensions change are called sparse changes , and they are the subject of much current interest (Chan, ; Liu et al, ; Wang et al, ; Wang & Samworth, ; Xie & Siegmund, ). Third, we measure sensitivity by the normal Hellinger distance between the marginal distributions of projections before and after a change, whereas Kuncheva and Faithfull () use the normal Bhattacharyya distance.…”

Section: Introductionmentioning

confidence: 99%

Which principal components are most sensitive in the change detection problem?

Tveten

2019

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Principal component analysis (PCA) is often used in anomaly detection and statistical process control tasks. For bivariate normal data, we prove that the minor projection (the least varying projection) of the PCA‐rotated data is the most sensitive to distributional changes, where sensitivity is defined as the Hellinger distance between the projections' marginal distributions before and after a change. In particular, this is almost always the case if only one parameter of the bivariate normal distribution changes, that is, the change is sparse. Simulations indicate that the minor projections are the most sensitive for a large range of changes and pre‐change settings in higher dimensions as well, including changes that are very sparse. This motivates using only a few of the minor projections for detecting sparse distributional changes in high‐dimensional data.

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Section: Introductionmentioning

confidence: 99%

Which principal components are most sensitive in the change detection problem?

Tveten

2019

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“…The asymptotic optimality of a related mixture statistic is established in [3]. Extensions and modifications of the mixture statistic that lead to optimal detection are considered in [1].…”

Section: Introductionmentioning

confidence: 99%

“…In the above references [18,1], the change-point is assumed to cause a shift in the means of the observations by the affected sensors, which is good for modeling an abrupt change. However, in many applications above, the changepoint is an onset of system degradation, which causes a gradual change to the sensor observations.…”

Section: Introductionmentioning

confidence: 99%

Multi-sensor slope change detection

2016

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We develop a mixture procedure for multi-sensor systems to monitor data streams for a change-point that causes a gradual degradation to a subset of the streams. Observations are assumed to be initially normal random variables with known constant means and variances. After the change-point, observations in the subset will have increasing or decreasing means. The subset and the rate-of-changes are unknown. Our procedure uses a mixture statistics, which assumes that each sensor is affected by the change-point with probability p 0 . Analytic expressions are obtained for the average run length (ARL) and the expected detection delay (EDD) of the mixture procedure, which are demonstrated to be quite accurate numerically. We establish the asymptotic optimality of the mixture procedure. Numerical examples demonstrate the good performance of the proposed procedure. We also discuss an adaptive mixture procedure using empirical Bayes. This paper extends our earlier work on detecting an abrupt change-point that causes a mean-shift, by tackling the challenges posed by the non-stationarity of the slope-change problem.

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“…A mixture statistic which utilizes this sparsity structure of this problem is presented in [5]. The asymptotic optimality of a related mixture statistic is established in [6] and extensions and modifications of the mixture statistic that lead to optimal detection is considered in [7].…”

Section: Introductionmentioning

confidence: 99%

“…In the above references [5]- [7], the change-point is assumed to cause a shift in the mean of the affected sensors, and this is good for modeling an abrupt change. However, in many applications above, the change result in an onset of the system degradation, which may cause a gradual change to the sensor observations, and we set-out to detect the gradual change.…”

Section: Introductionmentioning

confidence: 99%

Multi-sensor gradual change detection

Cao

Xie

2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We develop a mixture procedure to monitor parallel streams of data for a change-point that causes gradual change of a subset of data streams. We model the gradual change as a change in the trends of the affected data streams. Observations are assumed initially to be independent standard normal random variables with zero mean. After a change-point the observations in a subset of the streams of data have mean values that increase or decrease with time. The rate of change for the affected sensors may be different for the affected sensors. The subset and the post-change means are unknown but we assume the number of affected sensors is small. Our procedure uses a mixture statistics which hypothesizes an assumed fraction p0 of affected data streams. An analytic expression is obtained for the average run length (ARL) when there is no change and is shown by simulations to be very accurate. Similarly, an approximation for the expected detection delay (EDD) after a change-point is also obtained. Numerical examples based on real-data demonstrate the good performance of the proposed procedure on real data.

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Optimal sequential detection in multi-stream data

Cited by 46 publications

References 16 publications

Which principal components are most sensitive in the change detection problem?

Which principal components are most sensitive in the change detection problem?

Multi-sensor slope change detection

Multi-sensor gradual change detection

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