Related papers: Variational Gaussian approximation of the Kushner …
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
In the present paper we consider the semiclassical magnetic Schr\"odinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the time-dependent Schr\"odinger equation is approximated…
We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally,…
Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the…
On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains…
We propose a transfer principle to study the adapted 2-Wasserstein distance between stochastic processes. First, we obtain an explicit formula for the distance between real-valued mean-square continuous Gaussian processes by introducing the…
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an…
We consider the problem of estimating a continuous-time Gauss-Markov source process observed through a vector Gaussian channel with an adjustable channel gain matrix. For a given (generally time-varying) channel gain matrix, we provide…
We develop a non-perturbative method to derive the probability distribution $P(\delta_R)$ of the density contrast within spherical cells in the quasi-linear regime. Indeed, since this corresponds to a rare-event limit a steepest-descent…
Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…
Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…
Recently, several studies proposed non-linear transformations, such as a logarithmic or Gaussianization transformation, as efficient tools to recapture information about the (Gaussian) initial conditions. During non-linear evolution, part…
Natural gradients can improve convergence in stochastic variational inference significantly but inverting the Fisher information matrix is daunting in high dimensions. Moreover, in Gaussian variational approximation, natural gradient…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
The problem of estimating the dynamic direction of arrival of far field signals impinging on a uniform linear array, with mutual coupling effects, is addressed. This work proposes two novel approaches able to provide accurate solutions,…
The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic…
Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…