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Optimal transportation distances are a fundamental family of parameterized for histograms. Despite their appealing theoretical properties, performance in retrieval tasks and intuitive formulation, their involves the resolution of a linear program whose cost is whenever the histograms' dimension exceeds a few hundreds. We in this work a new family of optimal transportation distances that look transportation problems from a maximum-entropy perspective. We smooth the optimal transportation problem with an entropic regularization term, show that the resulting optimum is also a distance which can be computed Sinkhorn-Knopp's matrix scaling algorithm at a speed that is several of magnitude faster than that of transportation solvers. We also report performance over classical optimal transportation distances on the benchmark problem.
Marco Cuturi (Tue,) studied this question.