Related papers: Expanding the Standard Diffusion Process to Specif…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…
Diffusion models typically operate in the standard framework of generative modelling by producing continuously-valued datapoints. To this end, they rely on a progressive Gaussian smoothing of the original data distribution, which admits an…
Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…
The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
Asymmetric, non-Gaussian probability distributions are often observed in the analysis of natural and engineering datasets. The lognormal distribution is a standard model for data with skewed frequency histograms and fat tails. However, the…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We construct a class of stochastic differential equations driven by White Gaussian noise sources whose solutions can be drawn from skewed Gaussian probability laws, here referred as skew-Normal diffusion (SKN) processes. The non-Gaussian…
Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…
Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) remains challenging. Because physical domains are naturally…
The basic goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript we focus on the analysis of non-Gaussian distributed data. In the…
Stochastic differential equations (SDEs) using jump-diffusion processes describe many natural phenomena at the microscopic level. Since they are commonly used to model economic and financial evolutions, the calibration and optimal control…
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is…
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…
Although there is much recent work developing flexible variational methods for Bayesian computation, Gaussian approximations with structured covariance matrices are often preferred computationally in high-dimensional settings. This paper…
Diffusion models have proven effective for various applications such as images, audio and graph generation. Other important applications are image super-resolution and the solution of inverse problems. More recently, some works have used…