Measuring Time-Series Dataset Similarity using Wasserstein Distance

2025-07-29

AI Summary

This paper addresses the challenge of quantifying similarity among time-series datasets. We propose a novel distribution-based similarity measure: each dataset is modeled as a multivariate Gaussian distribution, and their dissimilarity is captured via the Wasserstein distance, augmented with empirical covariance estimation and distributional geometric analysis. To our knowledge, this is the first work to apply the Wasserstein distance at the dataset level for time-series similarity modeling. The method effectively captures distributional shifts and supports downstream tasks including model selection, fine-tuning, and visualization. Experiments demonstrate that the proposed metric exhibits strong correlation (Pearson *r* > 0.60) with inference loss of base models under out-of-distribution and transfer learning settings. Consequently, it significantly improves the efficiency of model evaluation and enhances predictive capability for generalization performance.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

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).

Problem

• Measure similarity of time-series datasets using Wasserstein distance
• Model selection and finetuning for time-series foundation models
• Evaluate performance in out-of-distribution and transfer learning scenarios

Innovation

• Uses Wasserstein distance for dataset similarity
• Models datasets as multivariate normal distributions
• Correlates distance with foundation model performance