# Measuring Time-Series Dataset Similarity using Wasserstein Distance

arXiv: https://arxiv.org/abs/2507.22189 · HTML: https://mlsanity.com/paper/2507.22189/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 50 references that are in the map.
- First posted on arXiv 29 Jul 2025.

## Builds on (most cited first, 30 of 33)

- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting](https://mlsanity.com/paper/2310.09751/) (2023)
- [Improved Distribution Matching for Dataset Condensation](https://mlsanity.com/paper/2307.09742/) (2023)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2310.08278/) (2023)
- [MetaShift: A Dataset of Datasets for Evaluating Contextual Distribution Shifts and Training Conflicts](https://mlsanity.com/paper/2202.06523/) (2022)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Time Series Prediction using Deep Learning Methods in Healthcare](https://mlsanity.com/paper/2108.13461/) (2021)
- [Statistical optimal transport](https://mlsanity.com/paper/2407.18163/) (2024)
- [GluonTS: Probabilistic Time Series Models in Python](https://mlsanity.com/paper/1906.05264/) (2019)
- [A review on distance based time series classification](https://mlsanity.com/paper/1806.04509/) (2018)
- [Differentiable Divergences Between Time Series](https://mlsanity.com/paper/2010.08354/) (2020)
- [Wasserstein Divergence for GANs](https://mlsanity.com/paper/1712.01026/) (2017)
- [Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes](https://mlsanity.com/paper/1801.01990/) (2018)
- [DANCE: Dual-View Distribution Alignment for Dataset Condensation](https://mlsanity.com/paper/2406.01063/) (2024)
- [Understanding the Transferability of Representations via Task-Relatedness](https://mlsanity.com/paper/2307.00823/) (2023)
- [An Integrated Transportation Distance Between Kernels and Approximate Dynamic Risk Evaluation in Markov Systems](https://mlsanity.com/paper/2311.06645/) (2023)
- [Accuracy on the wrong line: On the pitfalls of noisy data for out-of-distribution generalisation](https://mlsanity.com/paper/2406.19049/) (2024)
- [Clustering time series under the Fr'echet distance](https://mlsanity.com/paper/1512.04349/) (2015)
- [DRGraph: An Efficient Graph Layout Algorithm for Large-scale Graphs by Dimensionality Reduction](https://mlsanity.com/paper/2008.07799/) (2020)
- [Log-Euclidean Signatures for Intrinsic Distances Between Unaligned Datasets](https://mlsanity.com/paper/2202.01671/) (2022)
- [Distribution-on-Distribution Regression with Wasserstein Metric: Multivariate Gaussian Case](https://mlsanity.com/paper/2307.06137/) (2023)

## Built on by (most cited first, 1 of 1)

- [TSDS-Toolbox: A Toolbox for Measuring Time-Series Dataset Similarity](https://mlsanity.com/paper/2608.08119/) (2026)

## Abstract (arXiv)

The emergence of time-series foundation model research elevates the growing need to measure the (dis)similarity of time-series datasets. A time-series dataset similarity measure aids research in multiple ways, including model selection, finetuning, and visualization. In this paper, we propose a distribution-based method to measure time-series dataset similarity by leveraging the Wasserstein distance. We consider a time-series dataset an empirical instantiation of an underlying multivariate normal distribution (MVN). The similarity between two time-series datasets is thus computed as the Wasserstein distance between their corresponding MVNs. Comprehensive experiments and visualization show the effectiveness of our approach. Specifically, we show how the Wasserstein distance helps identify similar time-series datasets and facilitates inference performance estimation of foundation models in both out-of-distribution and transfer learning evaluation, with high correlations between our proposed measure and the inference loss (>0.60).