Convex set detection

Brunel, Victor-Emmanuel

doi:10.48550/arxiv.1404.6224

Cited by 3 publications

(10 citation statements)

References 12 publications

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“…Theorem 4.3 shows that under suitable d, the location of estimated change point is rate optimal (Brunel, 2014).…”

Section: Minimax Localization Ratementioning

confidence: 99%

Weighted-Graph-Based Change Point Detection

Nie,

Nicolae

2021

Preprint

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We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when at most one change point occurs and generalize them to multiple change points settings. The proposed statistics leverage edge weight information in the graphs, exhibiting substantial improvements in testing power and localization accuracy in simulations. We derive the null limiting distribution, provide accurate analytic approximations to control type I error, and establish theoretical guarantees on the power consistency under contiguous alternatives for the one change point setting, as well as the minimax localization rate. In the multiple change points setting, the asymptotic correctness of the number and location of change points are also guaranteed. The methods are illustrated on the MIT proximity network data.

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“…Theorem 4.3 shows that under suitable d, the location of estimated change point is rate optimal (Brunel, 2014).…”

Section: Minimax Localization Ratementioning

confidence: 99%

Weighted-Graph-Based Change Point Detection

Nie,

Nicolae

2021

Preprint

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“…In order to determine the most relevant way to integrate this knowledge, we have used an exact expression for the probability distribution function as well as an exponential inequality for the supremum of Poisson processes with shift, both due to Pyke [89,Equation (6) and Theorem 3]. This has led to a new procedure which is rather atypical regarding the other tests of this paper, and which can be related to Brunel's [19] scan test in the Gaussian set-up.…”

Section: Known Change Heightmentioning

confidence: 99%

“…But the procedures introduced in this work go beyond the scope of the present minimax testing study as they further address the twin problems of detecting and localising multiple change-points. In the case where the change height is known, equal to 1, Brunel [19] constructed a test based on a scanning of the shifted test statistic τ +ℓ−1 i=τ Y i − ℓ/2, which is consistent as soon as ℓ/ log n → +∞. Still considering the ℓ 2 metric on the mean vectors, but considering, among piecewise monotone signals estimation problems, the special problem of detecting a jump from an unknown constant mean, Gao et al [54] obtained a lower bound of order √ log log n. More precisely, they proved that no test can reliably detect Y such that E [ Y i ] = δ1 {i∈[τ,n]} (with τ ∈ {2, .…”

Section: Introductionmentioning

confidence: 99%

Minimax and adaptive tests for detecting abrupt and possibly transitory changes in a Poisson process

Fromont¹,

Grela²,

Guével³

2021

Preprint

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Motivated by applications in cybersecurity and epidemiology, we consider the problem of detecting an abrupt change in the intensity of a Poisson process, characterised by a jump (non transitory change) or a bump (transitory change) from constant. We propose a complete study from the nonasymptotic minimax testing point of view, when the constant baseline intensity is known or unknown. The question of minimax adaptation with respect to each parameter (height, location, length) of the change is tackled, leading to a comprehensive overview of the various minimax separation rate regimes. We exhibit three such regimes and identify the factors of the two phase transitions, by giving the cost of adaptation to each parameter. For each alternative hypothesis, depending on the knowledge or not of each change parameter, we propose minimax or minimax adaptive tests based on linear statistics, close to CUSUM statistics, or quadratic statistics more adapted to the L 2 -distance considered in our minimax criteria and typically more powerful in practice, as our simulation study shows. When the change location or length is unknown, our adaptive tests are constructed from a scan aggregation principle combined with Bonferroni or min-p level correction, and a conditioning trick when the baseline intensity is unknown.

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“…Our procedure P n has no need to specify the parameter L or any other unknown parameters. (4) The LRS procedure has a computational complexity of O(nL). Depending on the choice of L, the complexity could be large.…”

Section: Block Signal Identification Under Gaussian White Noisementioning

confidence: 99%

“…It is also interesting to compare our results with other results in change-point detection settings. For most research in change-point detection area, they typically seek to find an rate optimal solution rather than an exact optimal solution, due to the more complex structure they consider, see for example [12] and [4]. Our signal identification problem has a slightly easier setting and we can achieve the exact optimal constant.…”

Section: Disucssionmentioning

confidence: 99%

Identifying the Support of Rectangular Signals in Gaussian Noise

Kou¹

2017

Preprint

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We consider the problem of identifying the support of the block signal in a sequence when both the length and the location of the block signal are unknown. The multivariate version of this problem is also considered, in which we try to identify the support of the rectangular signal in the hyperrectangle. We allow the length of the block signal to grow polynomially with the length of the sequence, which greatly generalizes the previous results in [16]. A statistical boundary above which the identification is possible is presented and an asymptotically optimal and computationally efficient procedure is proposed under Gaussian white noise in both the univariate and multivariate settings. The problem of block signal identification is shown to have the same statistical difficulty as the corresponding problem of detection in both the univariate and multivariate cases, in the sense that whenever we can detect the signal, we can identify the support of the signal. Some generalizations are also considered here: (1) We extend our theory to the case of multiple block signals.(2) We also discuss about the robust identification problem when the noise distribution is unspecified and the block signal identification problem under the exponential family setting.

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Convex set detection

Cited by 3 publications

References 12 publications

Weighted-Graph-Based Change Point Detection

Weighted-Graph-Based Change Point Detection

Minimax and adaptive tests for detecting abrupt and possibly transitory changes in a Poisson process

Identifying the Support of Rectangular Signals in Gaussian Noise

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