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Entropic Optimal Transport between Unbalanced Gaussian Measures has a Closed Form

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Academic year: 2021

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Figure 1: Numerical convergence the (n-samples) empirical estimation of OT(α n , β n ) computed using Sinkhorn’s algorithm towards the closed form of OT σ (α, β) and UOT σ (α, β) (the theoretical limit is dashed) given by Theorem 1 and Theorem 3 for random
Figure 3: Numerical convergence the (n-samples) empirical estimation of the theoretical mean µ and covariance H of theorem 3
Figure 4: Average run-time of Newton-Schulz and EVD to compute on CPUs and GPUs.
Figure 7: Bures, Sinkhorn-Bures, and Euclidean geodesics. Sinkhorn-Bures trajectories converge to Bures geodesics as σ goes to 0, and to Euclidean geodesics as σ goes to infinity.
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