# Optimal Nonparametric Multivariate Change Point Detection and Localization

title={Optimal Nonparametric Multivariate Change Point Detection and Localization},
author={Oscar Hernan Madrid Padilla and Yi Yu and Daren Wang and Alessandro Rinaldo},
journal={IEEE Transactions on Information Theory},
year={2022},
volume={68},
pages={1922-1944}
}
• Published 29 October 2019
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
We study the multivariate nonparametric change point detection problem, where the data are a sequence of independent $p$ -dimensional random vectors whose distributions are piecewise-constant with Lipschitz densities changing at unknown times, called change points. We quantify the size of the distributional change at any change point with the supremum norm of the difference between the corresponding densities. We are concerned with the localization task of estimating the positions of the change…

## Figures and Tables from this paper

Dynamic and heterogeneous treatment effects with abrupt changes
• Mathematics
• 2022
From personalised medicine to targeted advertising, it is an inherent task to provide a sequence of decisions with historical covariates and outcome data. This requires understanding of both the
Random Forests for Change Point Detection
• Computer Science, Mathematics
• 2022
In a large simulation study, the proposed changeforest method achieves improved empirical performance compared to existing multivariate nonparametric change point detection methods.
A review on minimax rates in change point detection and localisation.
• Yi Yu
• Computer Science
• 2020
This paper starts with the univariate mean change point analysis problem and review the state-of-the-art results in the literature, then moves on to more complex data types and investigates general principles behind the optimal procedures that lead to minimax rate-optimal results.
Localising change points in piecewise polynomials of general degrees
• Yi Yu
• Computer Science, Mathematics
• 2022
This paper proposes a two-step estimation procedure based on the (cid:2) 0 -penalisation and provides upper bounds on the localisation error and deriving global information-theoretic lower bounds, which show that the two- step estimators are nearly minimax rate-optimal.
Network change point localisation under local differential privacy
• Computer Science
• 2022
This paper investigates the fundamental limits in consistently localising change points under both node and edge privacy constraints, demonstrating interesting phase transition in terms of the signal-to-noise ratio condition, accompanied by polynomial-time algorithms.
High‐dimensional changepoint estimation with heterogeneous missingness
• Mathematics
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
• 2022
We propose a new method for changepoint estimation in partially observed, high‐dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first
Localising change points in piecewise polynomials of general degrees
• Computer Science, Mathematics
Electronic Journal of Statistics
• 2022
A two-step estimation procedure based on the $\ell_0$-penalisation and upper bounds on the localisation error are provided and it is shown that the estimator enjoys near optimally adaptive performance by attaining individual localisation errors depending on the level of smoothness at individual change points of the underlying signal.
High‐dimensional, multiscale online changepoint detection
• Computer Science
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
• 2022
A new method for high‐dimensional, online changepoint detection in settings where a p‐variate Gaussian data stream may undergo a change in mean, and it is proved that the patience, or average run length, of the procedure is at least at the desired nominal level.
Inference in high-dimensional online changepoint detection
• Mathematics, Computer Science
• 2021
An online algorithm is proposed that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor.
Scalable Bayesian change point detection with spike and slab priors
• Computer Science
• 2021
A Bayesian change point detection method is proposed, which is one of the fastest Bayesian methodologies, and it is more robust to misspecification of the error terms than the competing methods.

## References

SHOWING 1-10 OF 52 REFERENCES
Consistency results in multiple change-point problems
• Ph.D. thesis, Stanford University.
• 1992
Uniform Convergence Rate of the Kernel Density Estimator Adaptive to Intrinsic Volume Dimension
• Computer Science, Mathematics
ICML
• 2019
The volume dimension is proposed, called the volume dimension, to measure the intrinsic dimension of the support of a probability distribution based on the rates of decay of the probability of vanishing Euclidean balls and is useful for problems in geometric inference and topological data analysis.
A Kernel Multiple Change-point Algorithm via Model Selection
• Computer Science, Mathematics
J. Mach. Learn. Res.
• 2019
A penalty for choosing the number of change-points in the kernel-based method of Harchaoui and Capp{\'e} (2007) is built and a non-asymptotic oracle inequality is proved for the proposed method, thanks to a new concentration result for some function of Hilbert-space valued random variables.
A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data
• Mathematics
• 2013
The divisive method is shown to provide consistent estimates of both the number and the location of change points under standard regularity assumptions, and methods from cluster analysis are applied to assess performance and to allow simple comparisons of location estimates, even when the estimated number differs.
Probability and computing: randomization and probabilistic techniques in algorithms and data analysis
• Cambridge university press.
• 2017
Optimal nonparametric change point detection and localization.
• Computer Science, Mathematics
• 2019
It is proved that the procedure based on wild binary segmentation is nearly minimax rate-optimal and a phase transition in the space of model parameters that separates parameter combinations for which consistent localization is possible from the ones for which this task is statistical unfeasible is demonstrated.
Sequential Nonparametric Tests for a Change in Distribution: An Application to Detecting Radiological Anomalies
• Mathematics
Journal of the American Statistical Association
• 2018
ABSTRACT We propose a sequential nonparametric test for detecting a change in distribution, based on windowed Kolmogorov–Smirnov statistics. The approach is simple, robust, highly computationally