Derives a conformal Wasserstein-Fisher metric for belief revision costs from postulates on transport pricing and uniform nat pricing, yielding infinite cost at certainty and hyperbolic geometry on location-scale families.
Necessary optimality conditions for geodesics in weighted Wasserstein spaces
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abstract
The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These conditions have the form of a system of PDEs of the kind of the compressible Euler equations. Moreover, self-similar solutions to this system are discussed.
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cs.LG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A Transport-Based Geometry of Belief-Cost
Derives a conformal Wasserstein-Fisher metric for belief revision costs from postulates on transport pricing and uniform nat pricing, yielding infinite cost at certainty and hyperbolic geometry on location-scale families.