Deep generative models via explicit Wasserstein minimization
Chen, Yucheng
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https://hdl.handle.net/2142/104932
Description
Title
Deep generative models via explicit Wasserstein minimization
Author(s)
Chen, Yucheng
Issue Date
2019-04-25
Director of Research (if dissertation) or Advisor (if thesis)
Peng, Jian
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Deep Generative Models
Generative Adversarial Networks
Optimal Transport
Abstract
This thesis provides a procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source randomness of the network is a continuous distribution (the “semi-discrete” setting), then the Wasserstein distance is realized by a deterministic optimal transport mapping; (b) given an optimal transport mapping between a generator network and a target distribution, the Wasserstein distance may be decreased via a regression between the generated data and the mapped target points. The procedure here therefore alternates these two steps, forming an optimal transport and regressing against it, gradually adjusting the generator network towards the target distribution. Mathematically, this approach is shown to minimize the Wasserstein distance to both the empirical target distribution, and also its underlying population counterpart. Empirically, good performance is demonstrated on the training and testing sets of the MNIST and Thin-8 data. As a side product, the thesis proposes several effective metrics of measure performance of deep generative models. The thesis closes with a discussion of the unsuitability of the Wasserstein distance for certain tasks, as has been identified in prior work.
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