Penalization of barycenters for φ-exponential distributions
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In this paper we study the penalization of barycenters in the Wasserstein space for φ-exponential distributions. We obtain an explicit characterization of the barycenter in terms of the variances of the measures generalizing existing results for Gaussian measures. We then develop a gradient projection method for the computation of the barycenter establishing a Lipstchitz continuity for the gradient function. We also numerically show the influence of parameters and stability of the algorithm under small perturbation of data.
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