Time-series dataset similarity is defined via the Wasserstein distance between fitted multivariate normal distributions, and the distance shows partial correlation with foundation model inference loss.
Similarity Between Two Stochastic Differential Systems
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abstract
The main focus of this paper is to explore how much similarity between two stochastic differential systems. Motivated by the conjugate theory of stochastic dynamic systems, we study the relationship between two systems by finding homeomorphic mappings $K$. Particularly, we use the minimizer $K^*$ to measure the degree of similarity. Under appropriate assumptions, we give sufficient and necessary conditions for the existence of the minimizer $K^*$. The former result can be regarded as a strong law of large numbers, while the latter is a stochastic maximum principle. Finally, we provide different examples of stochastic systems and an application to stochastic Hartman Grobman theorem. Thus, the results illustrate what is the similarity, extending the conjugacy in stochastic dynamical systems.
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Measuring Time-Series Dataset Similarity using Wasserstein Distance
Time-series dataset similarity is defined via the Wasserstein distance between fitted multivariate normal distributions, and the distance shows partial correlation with foundation model inference loss.