Optimal nonparametric multivariate change point detection and localization

Padilla, Oscar Hernán Madrid; Chen, Yu; Wang, Daren; Rinaldo, Alessandro

doi:10.48550/arxiv.1910.13289

Cited by 9 publications

(11 citation statements)

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“…Several of these proposals require the calculation of numerous lasso (Tibshirani, 1996), graphical lasso (Friedman et al, 2008) or similar rather costly estimators. Another example would be multivariate non-parametric change point detection for which Kovács et al (2020) use random forests (Breiman, 2001) and other classifiers, Padilla et al (2019b) use kernel density estimation, while Matteson and James (2014) utilise energy distances. Overall, in all approaches requiring costly single fits, it is essential to keep the total length of search intervals as small as possible to make computations feasible and thus to have practically usable methods.…”

Section: Resultsmentioning

confidence: 99%

Seeded Binary Segmentation: A general methodology for fast and optimal change point detection

Kovács¹,

Li²,

Bühlmann³

et al. 2020

Preprint

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In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of background intervals, called seeded intervals, in which single change points are searched. The final selection of change points based on the candidates from seeded intervals can be done in various ways, adapted to the problem at hand. Thus, seeded binary segmentation is easy to adapt to a wide range of change point detection problems, let that be univariate, multivariate or even high-dimensional.We consider the univariate Gaussian change in mean setup in detail. For this specific case we show that seeded binary segmentation leads to a near-linear time approach (i.e. linear up to a logarithmic factor) independent of the underlying number of change points. Furthermore, using appropriate selection methods, the methodology is shown to be asymptotically minimax optimal. While computationally more efficient, the finite sample estimation performance remains competitive compared to state of the art procedures. Moreover, we illustrate the methodology for high-dimensional settings with an inverse covariance change point detection problem where our proposal leads to massive computational gains while still exhibiting good statistical performance.

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Section: Resultsmentioning

confidence: 99%

Seeded Binary Segmentation: A general methodology for fast and optimal change point detection

Kovács¹,

Li²,

Bühlmann³

et al. 2020

Preprint

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show abstract

“…where • ∞ is the sup-norm of a function. In Padilla et al (2019), a similar CUSUM was proposed in studying the nonparametric density change point detection problem. In our setting, we are interested in change points in the regression functions.…”

Section: Methodsmentioning

confidence: 99%

Locally private online change point detection

Berrett¹,

Yu²

2021

Preprint

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We study online change point detection problems under the constraint of local differential privacy (LDP) where, in particular, the statistician does not have access to the raw data. As a concrete problem, we study a multivariate nonparametric regression problem. At each time point t, the raw data are assumed to be of the form (X t , Y t ), where X t is a d-dimensional feature vector and Y t is a response variable. Our primary aim is to detect changes in the regression function m t (x) = E(Y t |X t = x) as soon as the change occurs. We provide algorithms which respect the LDP constraint, which control the false alarm probability, and which detect changes with a minimal (minimax rate-optimal) delay. To quantify the cost of privacy, we also present the optimal rate in the benchmark, non-private setting. These non-private results are also new to the literature and thus are interesting per se. In addition, we study the univariate mean online change point detection problem, under privacy constraints. This serves as the blueprint of studying more complicated private change point detection problems.

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“…For instance, as we mentioned before, in robust mean estimation problems under the Huber ε-contamination model, the value ε should be known in order to achieve optimal results in most algorithms and it is impossible to estimate ε when the contamination distribution is not specified [32]. Padilla et al [41] studied the nonparametric change point detection problems, which is also a type of robust change point detection problem, and the optimality results thereof rely on the kernel bandwidth h to be the same order as the minimal signal strength. In line with our discussions in Section 2, we consider the following two cases.…”

Section: Optimality Of the Arc Algorithmmentioning

confidence: 99%

Adversarially robust change point detection

Li¹,

Yu²

2021

Preprint

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Change point detection is becoming increasingly popular in many application areas. On one hand, most of the theoretically-justified methods are investigated in an ideal setting without model violations, or merely robust against identical heavy-tailed noise distribution across time and/or against isolate outliers; on the other hand, we are aware that there have been exponentially growing attacks from adversaries, who may pose systematic contamination on data to purposely create spurious change points or disguise true change points. In light of the timely need for a change point detection method that is robust against adversaries, we start with, arguably, the simplest univariate mean change point detection problem. The adversarial attacks are formulated through the Huber ε-contamination framework, which in particular allows the contamination distributions to be different at each time point. In this paper, we demonstrate a phase transition phenomenon in change point detection. This detection boundary is a function of the contamination proportion ε and is the first time shown in the literature. In addition, we derive the minimax-rate optimal localisation error rate, quantifying the cost of accuracy in terms of the contamination proportion. We propose a computationally feasible method, matching the minimax lower bound under certain conditions, saving for logarithmic factors. Extensive numerical experiments are conducted with comparisons to robust change point detection methods in the existing literature.

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Optimal nonparametric multivariate change point detection and localization

Cited by 9 publications

References 0 publications

Seeded Binary Segmentation: A general methodology for fast and optimal change point detection

Seeded Binary Segmentation: A general methodology for fast and optimal change point detection

Locally private online change point detection

Adversarially robust change point detection

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