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Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detection

arXiv 2202.06593 ↗First posted 14 Feb 2022stat.ML cs.LGcited by 0

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Abstract (arXiv)

We study statistical inference on the similarity/distance between two time-series under uncertain environment by considering a statistical hypothesis test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The sampling distribution of the DTW distance is too difficult to derive because it is obtained based on the solution of the DTW algorithm, which is complicated. To circumvent this difficulty, we propose to employ the conditional selective inference framework, which enables us to derive a valid inference method on the DTW distance. To our knowledge, this is the first method that can provide a valid p-value to quantify the statistical significance of the DTW distance, which is helpful for high-stake decision making such as abnormal time-series detection problems. We evaluate the performance of the proposed inference method on both synthetic and real-world datasets.

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References · 26

  1. 2017Soft-DTW: a Differentiable Loss Function for Time-Seriescited by 265
  2. 2020A review on outlier/anomaly detection in time series datacited by 187
  3. 2013Exact post-selection inference, with application to the lassocited by 90
  4. 2014Optimal Inference After Model Selectioncited by 63
  5. 2014Exact Post-Selection Inference for Sequential Regression Procedurescited by 47
  6. 2020Selective Inference for Hierarchical Clusteringcited by 37
  7. 2017Valid Inference Corrected for Outlier Removalcited by 25
  8. 2019Testing for a Change in Mean After Changepoint Detectioncited by 25
  9. 2020Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programmingcited by 25
  10. 2019Computing Valid p-values for Image Segmentation by Selective Inferencecited by 24
  11. 2021More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programmingcited by 24
  12. 2018More powerful post-selection inference, with application to the Lassocited by 22
14 more
  1. 2016Selective Inference for Group-Sparse Linear Modelscited by 21
  2. 2020Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inferencecited by 21
  3. 2018Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Datacited by 19
  4. 2014Selecting the number of principal components: estimation of the true rank of a noisy matrixcited by 18
  5. 2014A significance test for forward stepwise model selectioncited by 17
  6. 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuationcited by 16
  7. 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Modelcited by 15
  8. 2021Tree-Values: selective inference for regression treescited by 15
  9. 2017Selective Inference for Change Point Detection in Multi-dimensional Sequencescited by 11
  10. 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inferencecited by 10
  11. 2015Selective inference in regression models with groups of variablescited by 9
  12. 2019Approximate selective inference via maximum likelihoodcited by 8
  13. 2016Integrative Methods for Post-Selection Inference Under Convex Constraintscited by 7
  14. 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inferencecited by 7

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