# Segmentation of high dimensional means over multi-dimensional change points and connections to regression trees

arXiv: https://arxiv.org/abs/2105.10017 · HTML: https://mlsanity.com/paper/2105.10017/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 20 May 2021.

## Builds on (most cited first, 12 of 12)

- [Multiple-change-point detection for high dimensional time series via sparsified binary segmentation](https://mlsanity.com/paper/1611.08639/) (2016)
- [High-dimensional changepoint estimation via sparse projection](https://mlsanity.com/paper/1606.06246/) (2016)
- [Change Point Estimation in a Dynamic Stochastic Block Model](https://mlsanity.com/paper/1812.03090/) (2018)
- [Optimal Change Point Detection and Localization in Sparse Dynamic Networks](https://mlsanity.com/paper/1809.09602/) (2018)
- [Change-Point Estimation in High-Dimensional Markov Random Field Models](https://mlsanity.com/paper/1405.6176/) (2014)
- [Change-point detection in panel data via double CUSUM statistic](https://mlsanity.com/paper/1611.08631/) (2016)
- [Pivotal Estimation via Self-Normalization for High-Dimensional Linear Models with Error in Variables](https://mlsanity.com/paper/1708.08353/) (2017)
- [Change Point Estimation in Panel Data with Temporal and Cross-sectional Dependence](https://mlsanity.com/paper/1904.11101/) (2019)
- [Inference on the Change Point for High Dimensional Dynamic Graphical Models](https://mlsanity.com/paper/2005.09711/) (2020)
- [Inference for Change Points in High Dimensional Data via Self-Normalization](https://mlsanity.com/paper/1905.08446/) (2019)
- [Detection and estimation of parameters in high dimensional multiple change point regression models via ℓ1/ℓ0 regularization and discrete optimization](https://mlsanity.com/paper/1906.04396/) (2019)
- [Dating the Break in High-dimensional Data](https://mlsanity.com/paper/2002.04115/) (2020)

## Built on by (most cited first, 2 of 2)

- [Lattice partition recovery with dyadic CART](https://mlsanity.com/paper/2105.13504/) (2021)
- [Inference for Change Points in High Dimensional Mean Shift Models](https://mlsanity.com/paper/2107.09150/) (2021)

## Abstract (arXiv)

This article is motivated by the objective of providing a new analytically tractable and fully frequentist framework to characterize and implement regression trees while also allowing a multivariate (potentially high dimensional) response. The connection to regression trees is made by a high dimensional model with dynamic mean vectors over multi-dimensional change axes. Our theoretical analysis is carried out under a single two dimensional change point setting. An optimal rate of convergence of the proposed estimator is obtained, which in turn allows existence of limiting distributions. Distributional behavior of change point estimates are split into two distinct regimes, the limiting distributions under each regime is then characterized, in turn allowing construction of asymptotically valid confidence intervals for 2d-location of change. All results are obtained under a high dimensional scaling slog2 p=o(TwTh), where p is the response dimension, s is a sparsity parameter, and Tw,Th are sampling periods along change axes. We characterize full regression trees by defining a multiple multi-dimensional change point model. Natural extensions of the single 2d-change point estimation methodology are provided. Two applications, first on segmentation of it Infra-red astronomy satellite (IRAS) data and second to segmentation of digital images are provided. Methodology and theoretical results are supported with monte-carlo simulations.