Related papers: On Latent Distributions Without Finite Mean in Gen…

Exploring the dependence between covariates across distributions is crucial for many applications. Copulas serve as a powerful tool for modeling joint variable dependencies and have been effectively applied in various practical contexts due…

Data is commonly stored in tabular format. Several fields of research are prone to small imbalanced tabular data. Supervised Machine Learning on such data is often difficult due to class imbalance. Synthetic data generation, i.e.,…

We study the problem of multimodal generative modelling of images based on generative adversarial networks (GANs). Despite the success of existing methods, they often ignore the underlying structure of vision data or its multimodal…

This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Given a set of $K$ probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify…

Class imbalance remains a major challenge in machine learning, especially for high-dimensional biomedical data where nonlinear manifold structures dominate. Traditional oversampling methods such as SMOTE rely on local linear interpolation,…

In this work, we extend the Da Prato-Grisvard theory of maximal regularity estimates for sectorial operators in interpolation spaces. Specifically, for any generator $-A$ of an analytic semigroup on a Banach space $X$, we identify the…

When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…

Sampling from generative models has become a crucial tool for applications like data synthesis and augmentation. Diffusion, Flow Matching and Continuous Normalising Flows have shown effectiveness across various modalities, and rely on…

We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…

Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…

Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of…

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of…

Recent work has shown that deep generative models assign higher likelihood to out-of-distribution inputs than to training data. We show that a factor underlying this phenomenon is a mismatch between the nature of the prior distribution and…

Deep generative models offer powerful tools for multivariate data analysis, but their black-box architectures are often unidentified and difficult to interpret. We introduce the Deep Discrete Encoder (DDE) Copula, an identifiable and…

Deep neural networks achieve superior performance for learning from independent and identically distributed (i.i.d.) data. However, their performance deteriorates significantly when handling out-of-distribution (OoD) data, where the…

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…