# Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programming

arXiv: https://arxiv.org/abs/2002.09132 · HTML: https://mlsanity.com/paper/2002.09132/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2020.

## Built on by (most cited first, 25 of 25)

- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
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- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation](https://mlsanity.com/paper/2104.10840/) (2021)
- [Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference](https://mlsanity.com/paper/2110.08989/) (2021)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Exact Statistical Inference for the Wasserstein Distance by Selective Inference](https://mlsanity.com/paper/2109.14206/) (2021)
- [Statistical Test for Anomaly Detections by Variational Auto-Encoders](https://mlsanity.com/paper/2402.03724/) (2024)
- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [Statistical Test for Attention Map in Vision Transformer](https://mlsanity.com/paper/2401.08169/) (2024)
- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [Statistical Test for Feature Selection Pipelines by Selective Inference](https://mlsanity.com/paper/2406.18902/) (2024)
- [Statistical Test for Auto Feature Engineering by Selective Inference](https://mlsanity.com/paper/2410.19768/) (2024)
- [Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inference](https://mlsanity.com/paper/2502.12978/) (2025)
- [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)
- [A Confidence Machine for Sparse High-Order Interaction Model](https://mlsanity.com/paper/2205.14317/) (2022)
- [Bounded P-values in Parametric Programming-based Selective Inference](https://mlsanity.com/paper/2307.11351/) (2023)
- [Unsupervised Text Segmentation via Kernel Change-Point Detection on Sentence Embeddings](https://mlsanity.com/paper/2601.18788/) (2026)
- [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)
- [Consistent Kernel Change-Point Detection under m-Dependence for Text Segmentation](https://mlsanity.com/paper/2510.03437/) (2025)
- [Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathology](https://mlsanity.com/paper/2609.31712/) (2026)
- [Post-Anomaly Detection Inference for Deep SVDD](https://mlsanity.com/paper/2609.37935/) (2026)

## Abstract (arXiv)

There is a vast body of literature related to methods for detecting changepoints (CP). However, less attention has been paid to assessing the statistical reliability of the detected CPs. In this paper, we introduce a novel method to perform statistical inference on the significance of the CPs, estimated by a Dynamic Programming (DP)-based optimal CP detection algorithm. Based on the selective inference (SI) framework, we propose an exact (non-asymptotic) approach to compute valid p-values for testing the significance of the CPs. Although it is well-known that SI has low statistical power because of over-conditioning, we address this disadvantage by introducing parametric programming techniques. Then, we propose an efficient method to conduct SI with the minimum amount of conditioning, leading to high statistical power. We conduct experiments on both synthetic and real-world datasets, through which we offer evidence that our proposed method is more powerful than existing methods, has decent performance in terms of computational efficiency, and provides good results in many practical applications.