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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…

We propose a new generative model, Cramer-Wold Autoencoder (CWAE). Following WAE, we directly encourage normality of the latent space. Our paper uses also the recent idea from Sliced WAE (SWAE) model, which uses one-dimensional projections…

The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…

The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…

Maximum mean discrepancy (MMD) has been successfully applied to learn deep generative models for characterizing a joint distribution of variables via kernel mean embedding. In this paper, we present conditional generative moment- matching…

Current advances in next generation sequencing techniques have allowed researchers to conduct comprehensive research on microbiome and human diseases, with recent studies identifying associations between human microbiome and health outcomes…

Quantifying degrees of fusion and separability between data groups in representation space is a fundamental problem in representation learning, particularly under domain shift. A meaningful metric should capture fusion-altering factors like…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

We show how a Cram\'er-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributions drawn from the same family. Using this abstract result,…

The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature…

Distance-based clustering and classification are widely used in various fields to group mixed numeric and categorical data. In many algorithms, a predefined distance measurement is used to cluster data points based on their dissimilarity.…

Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…

Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

In recent years, we have witnessed a surge of interests in learning a suitable distance metric from weakly supervised data. Most existing methods aim to pull all the similar samples closer while push the dissimilar ones as far as possible.…

Recent advances in generative modeling have led to an increased interest in the study of statistical divergences as means of model comparison. Commonly used evaluation methods, such as the Frechet Inception Distance (FID), correlate well…

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…