A Statistical Soft-DTW Similarity Based on the Wasserstein Distance

Abstract

We propose a new statistical soft-dtw similarity, namely the Wasserstein with Statistical Prior for Soft-DTW (WaSPS-DTW). Given a statistical model, the WaSPS-DTW computes a similarity from samples of a time series by leveraging the squared 2-Wasserstein distance between the thought probability distributions. We show that the WaSPS can be computed in a forward pass without adding much complexity to the original dynamic programming recursion. Furthermore, to integrate the WaSPS in optimization based scheme, we bring together the necessary tools to derive a backward recursion for differentiation of the proposed similarity. We consider the family of Weibull distribution and derive the aformentioned framework for a generic Weibull pdf from which we explicit the case of the exponential distribution. Finally, we apply the newly proposed metric to a classification task on a river discharge datasets modeled by an exponential distribution. The proposed similarity shows significant improvements compared to standard DTW discrepancy in performance qualitatively and quantitatively by almost ∼ 12%.

BibTeX

@inproceedings{gallet202605529554,
  title       = {A Statistical Soft-DTW Similarity Based on the Wasserstein Distance},
  author      = {Matthieu Gallet and Yassine Mhiri},
  booktitle   = {},
  year        = {2026},
  url         = {https://hal.science/hal-05529554v1},
}