Generative Modeling for Tabular Data via Penalized Optimal Transport Network

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.