Related papers: Black-box Variational Inference for Stochastic Dif…

We present a meta-algorithm for learning a posterior-inference algorithm for restricted probabilistic programs. Our meta-algorithm takes a training set of probabilistic programs that describe models with observations, and attempts to learn…

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…

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…

Deep stochastic processes have recently become a central paradigm for image enhancement, with many methods explicitly conditioning the stochastic trajectory on the degraded input. However, the relationship between these conditional…

Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…

Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…

Black-box variational inference (BBVI) with Gaussian mixture families offers a flexible approach for approximating complex posterior distributions without requiring gradients of the target density. However, standard numerical optimization…

We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…

Black Box Variational Inference is a promising framework in a succession of recent efforts to make Variational Inference more ``black box". However, in basic version it either fails to converge due to instability or requires some…

A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of theQmatrix for the discrete state…

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

In this paper we study model reduction of linear and bilinear quadratic stochastic control problems with parameter uncertainties. Specifically, we consider slow-fast systems with unknown diffusion coefficient and study the convergence of…

An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…

In structured additive distributional regression, the conditional distribution of the response variables given the covariate information and the vector of model parameters is modelled using a P-parametric probability density function where…

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects…

Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large…

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based…

Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…

We study an identification problem which estimates the parameters of the underlying random distribution for uncertain scalar conservation laws. The hyperbolic equations are discretized with the so-called discontinuous stochastic Galerkin…