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A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein distances. The developed method combines unsupervised learning…

Current techniques for Out-of-Distribution (OoD) detection predominantly rely on quantifying predictive uncertainty and incorporating model regularization during the training phase, using either real or synthetic OoD samples. However,…

Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…

The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first…

To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1…

Diabetic retinopathy grading is inherently ordinal and long-tailed, with minority stages being scarce, heterogeneous, and clinically critical to detect accurately. Conventional methods often rely on isotropic Gaussian priors and symmetric…

Density estimation, compression and data generation are crucial tasks in artificial intelligence. Variational Auto-Encoders (VAEs) constitute a single framework to achieve these goals. Here, we present a novel class of generative models,…

Variational Auto-encoders (VAEs) are deep generative latent variable models consisting of two components: a generative model that captures a data distribution p(x) by transforming a distribution p(z) over latent space, and an inference…

Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…

Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…

Variational autoencoders (VAEs) are widely used deep generative models capable of learning unsupervised latent representations of data. Such representations are often difficult to interpret or control. We consider the problem of…

Variational Autoencoders (VAEs) provide a theoretically-backed and popular framework for deep generative models. However, learning a VAE from data poses still unanswered theoretical questions and considerable practical challenges. In this…

VAE, or variational auto-encoder, compresses data into latent attributes, and generates new data of different varieties. VAE based on KL divergence has been considered as an effective technique for data augmentation. In this paper, we…

We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…

Conditional sampling of variational autoencoders (VAEs) is needed in various applications, such as missing data imputation, but is computationally intractable. A principled choice for asymptotically exact conditional sampling is…

Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…

Generative modelling is a key tool in unsupervised machine learning which has achieved stellar success in recent years. Despite this huge success, even the best generative models such as Generative Adversarial Networks (GANs) and…

In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder.…

Wasserstein autoencoders are effective for text generation. They do not however provide any control over the style and topic of the generated sentences if the dataset has multiple classes and includes different topics. In this work, we…

Even though auto-encoders (AEs) have the desirable property of learning compact representations without labels and have been widely applied to out-of-distribution (OoD) detection, they are generally still poorly understood and are used…