Abstract This project introduces an ongoing research to generate samples from a data set where the distribution is unknown. This project keeps focus on mass transportation approach to handle the problem. First, preliminaries on mass transportation problem and gradient flows on probability measures will be briefly introduced. Then, particle descent algorithm which is equipped with a flexible measure of distance will be introduced. The experiments on the low dimensional examples elaborate the dependency of this measure of distance on the target probability distribution. Strengths of this work comes from the flexible choice of the measure of distance and an interpolated behavior between f-divergences and Γ-intergral probability metrics. Also, the efficiency of this algorithm will be seen by comparing the convergence of a different algorithm, generative adversarial network. Then, a different approach fueled by Markov chain monte carlo will be briefly discussed in application of sample generation in a high dimensional data such as image data.

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