Optimal change point detection in Gaussian processes

Keshavarz, Hossein; Scott, Clayton; Nguyen, Xuan Long

doi:10.1016/j.jspi.2017.09.003

Cited by 23 publications

(16 citation statements)

References 52 publications

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“…From a theoretical point of view, asymptotic consistency, as described in Definition 1, has been demonstrated, in the case of a single change point, first with Gaussian distribution (fixed variance), then for several specific distributions, e.g. Gaussian with mean and scale shifts [3,6,51,57], discrete distributions [49], etc. The case with multiple change points has been tackled later.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Selective review of offline change point detection methods

2020

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This article presents a selective survey of algorithms for the offline detection of multiple change points in multivariate time series. A general yet structuring methodological strategy is adopted to organize this vast body of work. More precisely, detection algorithms considered in this review are characterized by three elements: a cost function, a search method and a constraint on the number of changes. Each of those elements is described, reviewed and discussed separately. Implementations of the main algorithms described in this article are provided within a Python package called ruptures.

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Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Selective review of offline change point detection methods

2020

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“…It is known that (see e.g., [12,23]) for any bounded region D ⊂ R d with d ≤ 3, the Matern covariance models with parameters (φ 1 , ρ 1 ) and (φ 2 , ρ 2 ) yield absolutely continuous measures (with respect to each other) whenever φ 1 ρ −2ν…”

Section: The Local Inversion-free (Lif) Algorithmmentioning

confidence: 99%

Local inversion-free estimation of spatial Gaussian processes

Keshavarz¹,

Nguyen²,

Scott³

2019

Electron. J. Statist.

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Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for large number of (possibly) irregularly spaced observations, due to the need to handle the inverse of ill-conditioned and large covariance matrices. Extending the "inversion-free" method of Anitescu, Chen and Stein [1], we investigate a broad class of covariance parameter estimation based on inversion-free surrogate losses and block diagonal approximation schemes of the covariance structure. This class of estimators yields a spectrum for negotiating the trade-off between statistical accuracy and computational cost. We present fixed-domain asymptotic properties of our proposed method, establishing √ n-consistency and asymptotic normality results for isotropic Matern Gaussian processes observed on a multi-dimensional and irregular lattice. Simulation studies are also presented for assessing the scalability and statistical efficiency of the proposed algorithm for large data sets.MSC 2010 subject classifications: Primary 62M30, 62M40; secondary 60G15. We are grateful to Mihai Anitescu and Michael Stein for valuable discussions and suggestions. 1 arXiv:1811.12602v3 [math.ST] 7 Jul 2019 2. Preconditioning and inversion-free surrogate loss 2.1. Gaussian processes observed on irregular lattices Consider a zero mean, real valued, and stationary Gaussian process G on domain D, where D is a bounded subset of R d such as [0, 1]d . The dependence structure of G is typically parametrized by a variance parameter φ 0 > 0 and a (correlation) range parameter ρ 0 . Specifically, if G is a geometric anisotropic process on D, then there are a fully known covariance function K and a matrix ρ 0 ∈ R d×d such thatThe objective is to estimate the microergodic parameters of the covariance function, given n measurements from one realization of G at locations D n = {s 1 , . . . , s n } ⊂ D. Throughout the paper, we assume that ρ 0 2 2 .However throughout the paper and for simplifying the theoretical analysis, we only consider the case of non-overlapping bins. It will also be assumed that w i = 1 for all i ∈ {1, . . . , b n }.Remark 3.2. It is informative to take an alternative viewpoint of the LIF objective function in (3.2) as corresponding to a block diagonal approximation of the covariance matrix. Interestingly, as a consequence of the asymptotic theory developed in the next section, this approximation does not affect the asymptotic estimation rate, but it can substantially help to speed up the computation. The block diagonal approximation of K n,m (ρ) corresponding to partitioning scheme B, to be denoted by K B n,m (ρ), can be described as follows. Choose any s, s ∈ D n , and let t, t denote the index of the elements in B containing s and s , i.e., s ∈ B t and s ∈ B t . The entries of K B n,m (ρ) can be equivalently represented by K B n,m (ρ) s,s = [K n,m (ρ)] s,s 1 {t=t } .Remark 4.3. It has been discus...

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“…The criteria proposed in recent years include the Bayesian Information Criterion (BIC) [ 10 ], the Hausdorff distance [ 11 ], the Kullback–Leibler divergence [ 12 , 13 ], the novelty score [ 14 ], and so on. The BIC based audio segmentation and its variations [ 15 , 16 ] are popular in audio segmentation because of the low calculation and high flexibility.…”

Section: Introductionmentioning

confidence: 99%

Segmentation Method for Ship-Radiated Noise Using the Generalized Likelihood Ratio Test on an Ordinal Pattern Distribution

Shen

Zhang

et al. 2020

Entropy

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Due to the diversity of ship-radiated noise (SRN), audio segmentation is an essential procedure in the ship statuses/categories identification. However, the existing segmentation methods are not suitable for the SRN because of the lack of prior knowledge. In this paper, by a generalized likelihood ratio (GLR) test on the ordinal pattern distribution (OPD), we proposed a segmentation criterion and introduce it into single change-point detection (SCPD) and multiple change-points detection (MCPD) for SRN. The proposed method is free from the acoustic feature extraction and the corresponding probability distribution estimation. In addition, according to the sequential structure of ordinal patterns, the OPD is efficiently estimated on a series of analysis windows. By comparison with the Bayesian Information Criterion (BIC) based segmentation method, we evaluate the performance of the proposed method on both synthetic signals and real-world SRN. The segmentation results on synthetic signals show that the proposed method estimates the number and location of the change-points more accurately. The classification results on real-world SRN show that our method obtains more distinguishable segments, which verifies its effectiveness in SRN segmentation.

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Optimal change point detection in Gaussian processes

Cited by 23 publications

References 52 publications

Selective review of offline change point detection methods

Selective review of offline change point detection methods

Local inversion-free estimation of spatial Gaussian processes

Segmentation Method for Ship-Radiated Noise Using the Generalized Likelihood Ratio Test on an Ordinal Pattern Distribution

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