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Adapted optimal transport between Gaussian processes in discrete time
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abstract
We derive explicitly the adapted $2$-Wasserstein distance between non-degenerate Gaussian distributions on $\mathbb{R}^N$ and characterize the optimal bicausal coupling(s). This leads to an adapted version of the Bures-Wasserstein distance on the space of positive definite matrices.
Forward citations
Cited by 2 Pith papers
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The Wasserstein Space of Stochastic Processes in Continuous Time
In continuous time, the Aldous, Hoover-Keisler, Hellwig, and optimal-stopping topologies on naturally filtered processes coincide and are metrized by an adapted Wasserstein distance, whose completion is the space of g...
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Comparing noisy neural population dynamics using optimal transport distances
A causal optimal transport distance between Gaussian processes compares noisy neural trajectories using their full temporal statistics, capturing differences that mean-based and marginal-based metrics miss.
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