  The task of precisely learning the probability distribution of rows within
tabular data and producing authentic synthetic samples is both crucial and
non-trivial. Wasserstein generative adversarial network (WGAN) marks a notable
improvement in generative modeling, addressing the challenges faced by its
predecessor, generative adversarial network. However, due to the mixed data
types and multimodalities prevalent in tabular data, the delicate equilibrium
between the generator and discriminator, as well as the inherent instability of
Wasserstein distance in high dimensions, WGAN often fails to produce
high-fidelity samples. To this end, we propose POTNet (Penalized Optimal
Transport Network), a generative deep neural network based on a novel, robust,
and interpretable marginally-penalized Wasserstein (MPW) loss. POTNet can
effectively model tabular data containing both categorical and continuous
features. Moreover, it offers the flexibility to condition on a subset of
features. We provide theoretical justifications for the motivation behind the
MPW loss. We also empirically demonstrate the effectiveness of our proposed
method on four different benchmarks across a variety of real-world and
simulated datasets. Our proposed model achieves orders of magnitude speedup
during the sampling stage compared to state-of-the-art generative models for
tabular data, thereby enabling efficient large-scale synthetic data generation.
