Asymptotic Guarantees for Generative Modeling Based on the Smooth Wasserstein Distance

Understand

Minimum distance estimation (MDE) gained recent attention as a formulation of (implicit) generative modeling.

• It considers minimizing, over model parameters, a statistical distance between the empirical data distribution and the model.
• This formulation lends itself well to theoretical analysis, but typical results are hindered by the curse of dimensionality.
• To overcome this and devise a scalable finite-sample statistical MDE theory, we adopt the framework of smooth 1-Wasserstein distance (SWD) $\mathsf{W}_1^{(\sigma)}$.