Related papers: Moment-Based Variational Inference for Stochastic …
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
We derive and present explicit algorithms to facilitate streamlined computing for variational inference for models containing higher level random effects. Existing literature, such as Lee and Wand (2016), is such that streamlined…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…
This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of the subordinated killed Brownian motion. The tempered…
Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…