# Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference

arXiv: https://arxiv.org/abs/2110.08989 · HTML: https://mlsanity.com/paper/2110.08989/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 60 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 19 of 19)

- [Deep, Convolutional, and Recurrent Models for Human Activity Recognition using Wearables](https://mlsanity.com/paper/1604.08880/) (2016)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Valid Inference Corrected for Outlier Removal](https://mlsanity.com/paper/1711.10635/) (2017)
- [Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programming](https://mlsanity.com/paper/2002.09132/) (2020)
- [Multiple-change-point detection for high dimensional time series via sparsified binary segmentation](https://mlsanity.com/paper/1611.08639/) (2016)
- [Computing Valid p-values for Image Segmentation by Selective Inference](https://mlsanity.com/paper/1906.00629/) (2019)
- [More powerful post-selection inference, with application to the Lasso](https://mlsanity.com/paper/1801.09037/) (2018)
- [Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Data](https://mlsanity.com/paper/1812.03644/) (2018)
- [A significance test for forward stepwise model selection](https://mlsanity.com/paper/1405.3920/) (2014)
- [Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation](https://mlsanity.com/paper/2104.10840/) (2021)
- [Post Selection Inference with Kernels](https://mlsanity.com/paper/1610.03725/) (2016)
- [Selective Inference for Change Point Detection in Multi-dimensional Sequences](https://mlsanity.com/paper/1706.00514/) (2017)
- [Post Selection Inference with Incomplete Maximum Mean Discrepancy Estimator](https://mlsanity.com/paper/1802.06226/) (2018)
- [Selective inference in regression models with groups of variables](https://mlsanity.com/paper/1511.01478/) (2015)
- [Selective review of offline change point detection methods](https://mlsanity.com/paper/1801.00718/) (2018)
- [Exact Statistical Inference for the Wasserstein Distance by Selective Inference](https://mlsanity.com/paper/2109.14206/) (2021)
- [Change-point detection in panel data via double CUSUM statistic](https://mlsanity.com/paper/1611.08631/) (2016)

## Built on by (most cited first, 10 of 10)

- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [Controllable RANSAC-based Anomaly Detection via Hypothesis Testing](https://mlsanity.com/paper/2410.15133/) (2024)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptation](https://mlsanity.com/paper/2508.07049/) (2025)
- [Post Hoc Inference for Component Attribution in Multivariate Change-Point Detection](https://mlsanity.com/paper/2607.14814/) (2026)
- [Bounded P-values in Parametric Programming-based Selective Inference](https://mlsanity.com/paper/2307.11351/) (2023)
- [Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detection](https://mlsanity.com/paper/2202.06593/) (2022)
- [Statistical Inference for Clustering-based Anomaly Detection](https://mlsanity.com/paper/2504.18633/) (2025)

## Abstract (arXiv)

In this paper, we study statistical inference of change-points (CPs) in multi-dimensional sequence. In CP detection from a multi-dimensional sequence, it is often desirable not only to detect the location, but also to identify the subset of the components in which the change occurs. Several algorithms have been proposed for such problems, but no valid exact inference method has been established to evaluate the statistical reliability of the detected locations and components. In this study, we propose a method that can guarantee the statistical reliability of both the location and the components of the detected changes. We demonstrate the effectiveness of the proposed method by applying it to the problems of genomic abnormality identification and human behavior analysis.