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SUMMARY:Nonparametric Generative Modeling via Optimal Transport and Diffus
 ions with Provable Guarantees - Umut Şimşekli\, Télécom Paristech
DTSTART:20190507T100000Z
DTEND:20190507T110000Z
UID:TALK122029@talks.cam.ac.uk
CONTACT:Eric T Nalisnick
DESCRIPTION:By building up on the recent theory that established the conne
 ction between implicit generative modeling and optimal transport\, in this
  talk\, I will present a novel parameter-free algorithm for learning the u
 nderlying distributions of complicated datasets and sampling from them. Th
 e proposed algorithm is based on a functional optimization problem\, which
  aims at finding a measure that is 'close to the data distribution as much
  as possible' and also 'expressive enough' for generative modeling purpose
 s. The problem will be formulated as a gradient flow in the space of proba
 bility measures. The connections between gradient flows and stochastic dif
 ferential equations will let us develop a computationally efficient algori
 thm for solving the optimization problem\, where the resulting algorithm w
 ill resemble the recent dynamics-based Markov Chain Monte Carlo algorithms
 . I will then present finite-time error guarantees for the proposed algori
 thm. I will finally present some experimental results\, which support our 
 theory and shows that our algorithm is able to capture the structure of ch
 allenging distributions. \n\nIf time permits\, I will also talk about poss
 ible extensions of this approach.\n\nThe talk will be based on these two a
 rticles: \n1) "Sliced-Wasserstein Flows":https://arxiv.org/abs/1806.08141\
 n2) "Generalized Sliced Wasserstein Distances":https://arxiv.org/abs/1902.
 00434
LOCATION:Engineering Department\, CBL Room BE-438.
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