Sliced generative models

In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case. Our experiments show that methods can be divided into two groups. First consists of methods which are a modification of standard normality tests, while the second is based on classical distances between samples. It turns out that both groups are correct generative models, but the second one gives a slightly faster decrease rate of Frechet Inception Distance (FID)

Joint Distributional Learning via Cramer-Wold Distance

The assumption of conditional independence among observed variables, primarily used in the Variational Autoencoder (VAE) decoder modeling, has limitations when dealing with high-dimensional datasets or complex correlation structures among observed variables. To address this issue, we introduced the Cramer-Wold distance regularization, which can be computed in a closed-form, to facilitate joint distributional learning for high-dimensional datasets. Additionally, we introduced a two-step learning method to enable flexible prior modeling and improve the alignment between the aggregated posterior and the prior distribution. Furthermore, we provide theoretical distinctions from existing methods within this category. To evaluate the synthetic data generation performance of our proposed approach, we conducted experiments on high-dimensional datasets with multiple categorical variables. Given that many readily available datasets and data science applications involve such datasets, our experiments demonstrate the effectiveness of our proposed methodology

Non-linear ICA based on Cramer-Wold metric

Non-linear source separation is a challenging open problem with many applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA) model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a simple, closed--form optimization target instead of a discriminator--based independence measure. Our results show that CW-ICA achieves comparable results to ANICA, while foregoing the need for adversarial training

Momentum Contrastive Autoencoder: Using Contrastive Learning for Latent Space Distribution Matching in WAE

Wasserstein autoencoder (WAE) shows that matching two distributions is equivalent to minimizing a simple autoencoder (AE) loss under the constraint that the latent space of this AE matches a pre-specified prior distribution. This latent space distribution matching is a core component of WAE, and a challenging task. In this paper, we propose to use the contrastive learning framework that has been shown to be effective for self-supervised representation learning, as a means to resolve this problem. We do so by exploiting the fact that contrastive learning objectives optimize the latent space distribution to be uniform over the unit hyper-sphere, which can be easily sampled from. We show that using the contrastive learning framework to optimize the WAE loss achieves faster convergence and more stable optimization compared with existing popular algorithms for WAE. This is also reflected in the FID scores on CelebA and CIFAR-10 datasets, and the realistic generated image quality on the CelebA-HQ dataset