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Nonparametric Generative Modeling via Optimal Transport and Diffusions with Provable Guarantees

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If you have a question about this talk, please contact Eric T Nalisnick.

By building up on the recent theory that established the connection between implicit generative modeling and optimal transport, in this talk, I will present a novel parameter-free algorithm for learning the underlying distributions of complicated datasets and sampling from them. The 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 purposes. The problem will be formulated as a gradient flow in the space of probability measures. The connections between gradient flows and stochastic differential equations will let us develop a computationally efficient algorithm for solving the optimization problem, where the resulting algorithm will resemble the recent dynamics-based Markov Chain Monte Carlo algorithms. I will then present finite-time error guarantees for the proposed algorithm. I will finally present some experimental results, which support our theory and shows that our algorithm is able to capture the structure of challenging distributions.

If time permits, I will also talk about possible extensions of this approach.

The talk will be based on these two articles: 1) Sliced-Wasserstein Flows 2) Generalized Sliced Wasserstein Distances

This talk is part of the Machine Learning @ CUED series.

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