Balanced Marginal and Joint Distributional Learning via Mixture
  Cramer-Wold Distance
Seunghwan An Sungchul Hong Jong-June Jeon
In the process of training a generative model, it becomes essential to
measure the discrepancy between two high-dimensional probability distributions:
the generative distribution and the ground-truth distribution of the observed
dataset. Recently, there has been growing interest in an approach that involves
slicing high-dimensional distributions, with the Cramer-Wold distance emerging
as a promising method. However, we have identified that the Cramer-Wold
distance primarily focuses on joint distributional learning, whereas
understanding marginal distributional patterns is crucial for effective
synthetic data generation. In this paper, we introduce a novel measure of
dissimilarity, the mixture Cramer-Wold distance. This measure enables us to
capture both marginal and joint distributional information simultaneously, as
it incorporates a mixture measure with point masses on standard basis vectors.
Building upon the mixture Cramer-Wold distance, we propose a new generative
model called CWDAE (Cramer-Wold Distributional AutoEncoder), which shows
remarkable performance in generating synthetic data when applied to real
tabular datasets. Furthermore, our model offers the flexibility to adjust the
level of data privacy with ease.