Measuring Time-Series Dataset Similarity using Wasserstein Distance
This addresses the need for dataset similarity measures in time-series foundation model research, aiding tasks like model selection and finetuning, but is incremental as it applies an existing distance metric to a new context.
The paper tackles the problem of measuring similarity between time-series datasets by proposing a method based on Wasserstein distance, representing datasets as multivariate normal distributions, and shows it effectively identifies similar datasets and estimates foundation model inference performance with correlations over 0.60.
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).