Efficient Generative Modeling via Penalized Optimal Transport Network

TL;DR

This paper introduces POTNet, a new deep generative model that uses penalized optimal transport to improve data generation quality, stability, and speed, especially in capturing complex data distributions.

Contribution

POTNet employs a marginally-penalized Wasserstein distance and a primal framework to enhance generative modeling, avoiding adversarial training issues and improving efficiency.

Findings

POTNet outperforms existing models in capturing data tail behaviors.

It achieves significant speedups in sample generation.

Theoretical bounds confirm its convergence and generalization capabilities.

Abstract

The generation of synthetic data with distributions that faithfully emulate the underlying data-generating mechanism holds paramount significance. Wasserstein Generative Adversarial Networks (WGANs) have emerged as a prominent tool for this task; however, due to the delicate equilibrium of the minimax formulation and the instability of Wasserstein distance in high dimensions, WGAN often manifests the pathological phenomenon of mode collapse. This results in generated samples that converge to a restricted set of outputs and fail to adequately capture the tail behaviors of the true distribution. Such limitations can lead to serious downstream consequences. To this end, we propose the Penalized Optimal Transport Network (POTNet), a versatile deep generative model based on the marginally-penalized Wasserstein (MPW) distance. Through the MPW distance, POTNet effectively leverages low-dimensional marginal information to guide the overall alignment of joint distributions. Furthermore, our primal-based framework enables direct evaluation of the MPW distance, thus eliminating the need for a critic network. This formulation circumvents training instabilities inherent in adversarial approaches and avoids the need for extensive parameter tuning. We derive a non-asymptotic bound on the generalization error of the MPW loss and establish convergence rates of the generative distribution learned by POTNet. Our theoretical analysis together with extensive empirical evaluations demonstrate the superior performance of POTNet in accurately capturing underlying data structures, including their tail behaviors and minor modalities. Moreover, our model achieves orders of magnitude speedup during the sampling stage compared to state-of-the-art alternatives, which enables computationally efficient large-scale synthetic data generation.