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SUMMARY:Gonzalo Mena (University of Oxford)
DESCRIPTION:“On the unreasonable effectiveness of Sinkhorn algorithm for learning permutations and entropic optimal transport” \nAbstract: Sinkhorn’s algorithm realizes the solution of entropy-regularized linear programs on certain matrix polytopes. In the past years\, the interest in this algorithm has grown considerably because of its usefulness as a tool for the modeling of permutations\, and because of its fundamental role in the solution of an entropic optimal transport problem\, also called the Schrödinger bridge. In this talk\, I will give an overview of my work in relation to these two areas.\nFirst\, regarding entropic optimal transport\, I will argue that this tool is valuable for deriving sensible statistical procedures. Indeed\, we show that it enjoys a substantially better sample complexity compared to optimal transport\, which suffers from the curse of dimensionality. Also\, in the more applied setup of model-based clustering we show that it can be used as an alternative to the log-likelihood\, since it has fewer bad local optima. Based on this observation\, we develop a new algorithm\, Sinkhorn-EM\, in which we only modify the E-step to solve an Entropic Optimal Transport problem. Our algorithm is shown to attain better practical performance.\nSecond\, regarding permutations\, I will describe some successful applications in Deep Learning\, and in neuroscience\, for the inference of neural identities in C.elegans worms. \nLinks\nhttps://arxiv.org/abs/1802.08665\nhttps://arxiv.org/abs/1905.11882\nhttps://arxiv.org/abs/2006.16548
URL:https://www.carloalberto.org/event/gonzalo-mena-university-of-oxford/
CATEGORIES:Seminars in Statistics
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