# Localizing Changes in High-Dimensional Regression Models

@inproceedings{Rinaldo2021LocalizingCI, title={Localizing Changes in High-Dimensional Regression Models}, author={Alessandro Rinaldo and Daren Wang and Qin Wen and Rebecca M. Willett and Yi Yu}, booktitle={AISTATS}, year={2021} }

This paper addresses the problem of localizing change points in high-dimensional linear regression models with piecewise constant regression coefficients. We develop a dynamic programming approach to estimate the locations of the change points whose performance improves upon the current state-of-the-art, even as the dimensionality, the sparsity of the regression coefficients, the temporal spacing between two consecutive change points, and the magnitude of the difference of two consecutive…

## 10 Citations

Denoising and change point localisation in piecewise-constant high-dimensional regression coefficients

- Computer ScienceAISTATS
- 2022

We study the theoretical properties of the fused lasso procedure originally proposed by Tibshirani et al. (2005) in the context of a linear regression model in which the regression coefficient are…

Localising change points in piecewise polynomials of general degrees

- 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.

Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach

- Mathematics, Computer Science
- 2022

A novel tail- Adaptive approach for simultaneous change point testing and estimation and combined with the wild binary segmentation technique, a new algorithm is proposed to detect multiple change points in a tail-adaptive manner.

Localising change points in piecewise polynomials of general degrees

- Computer Science, MathematicsElectronic 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.

Fast and Scalable Algorithm for Detection of Structural Breaks in Big VAR Models

- Computer ScienceJ. Comput. Graph. Stat.
- 2022

A novel procedure is proposed which leverages a block segmentation scheme (BSS) that reduces the number of model parameters to be estimated through a regularized least-square criterion and leads to significant computational gains without compromising on the statistical accuracy in identifying the number and location of the structural breaks.

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.

A review on minimax rates in change point detection and localisation.

- 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.

A Contrastive Approach to Online Change Point Detection

- MathematicsArXiv
- 2022

We suggest a novel procedure for online change point detection. Our approach expands an idea of maximizing a discrepancy measure between points from pre-change and post-change distributions. This…

Inference for Change Points in High Dimensional Mean Shift Models

- Mathematics
- 2021

We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares…

Inference on the Change Point in High Dimensional Dynamic Graphical Models

- Computer Science, Mathematics
- 2020

It is shown that the proposed estimator retains sufficient adaptivity against plugin estimates of the edge structure of the underlying graphical models, in order to yield an O(\psi^{-2}) rate of convergence of the change point estimator in the integer scale.

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