Related papers: Diffusion and Flow-based Copulas: Forgetting and R…

A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…

Regression analysis is one of the most popularly used statistical technique which only measures the direct effect of independent variables on dependent variable. Path analysis looks for both direct and indirect effects of independent…

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…

Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…

Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…

Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence…

Diffusion-based imitation learning improves Behavioral Cloning (BC) on multi-modal decision-making, but comes at the cost of significantly slower inference due to the recursion in the diffusion process. It urges us to design efficient…

Diffusion models are learning pattern-learning systems to model and sample from data distributions with three functional components namely the forward process, the reverse process, and the sampling process. The components of diffusion…

High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…

The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on…

This article presents factor copula approaches to model temporal dependency of non-Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a…

To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal…

Building higher-dimensional copulas is generally recognized as a difficult problem. Regular-vines using bivariate copulas provide a flexible class of high-dimensional dependency models. In large dimensions, the drawback of the model is the…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…

Diffusion models have achieved remarkable success in generating high-quality images thanks to their novel training procedures applied to unprecedented amounts of data. However, training a diffusion model from scratch is computationally…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

Verification and validation of fully automated vehicles is linked to an almost intractable challenge of reflecting the real world with all its interactions in a virtual environment. Influential stochastic parameters need to be extracted…

Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…

Copulas are a powerful tool to model dependence between the components of a random vector. One well-known class of copulas when working in two dimensions is the Farlie-GumbelMorgenstern (FGM) copula since their simple analytic shape enables…