Wasserstein projection onto displacement-convex sets yields a convex optimization approach to shape-constrained univariate density estimation for non-increasing and log-concave cases, with structural properties and a discretizable implementation.
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Provides asymptotic distributions for entropic OT plans and potentials under vanishing regularization and links self-transport barycentric projections to score functions.
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Shape-constrained density estimation with Wasserstein projection
Wasserstein projection onto displacement-convex sets yields a convex optimization approach to shape-constrained univariate density estimation for non-increasing and log-concave cases, with structural properties and a discretizable implementation.
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The entropic optimal (self-)transport problem: Limit distributions for decreasing regularization with application to score function estimation
Provides asymptotic distributions for entropic OT plans and potentials under vanishing regularization and links self-transport barycentric projections to score functions.