<ul><li>Estimating parameters from samples of optimal probability distribution is crucial in various applications.</li><li>A new approach involves minimizing sharpened Fenchel-Young losses to measure sub-optimality gap over measure space.</li><li>Method focuses on stability analysis with finite sample sizes, applicable to cost and potential function estimation in static and dynamic problems.</li><li>Specific applications include inverse unbalanced optimal transport and inverse gradient flow, validated with numerical experiments on Gaussian distributions.</li></ul>

Learning from Samples: Inverse Problems over measures via Sharpened Fenchel-Young Losses

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