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We investigate barycenters of Gaussian process laws in adapted Wasserstein space. The adapted Wasserstein distance refines classical optimal transport by enforcing compatibility of transport plans with the temporal flow of information, and…
We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…
In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full…
We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…
We consider a generalization of the classifier-based density-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. The problem with most loss functions used for this task is that they implicitly…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
Compared with word embedding based on point representation, distribution-based word embedding shows more flexibility in expressing uncertainty and therefore embeds richer semantic information when representing words. The Wasserstein…
High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…
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,…
To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
We study a mathematical model of a perturbed stratified shear mean flow in the presence of eddy coefficients of turbulent viscosity. We adopt the standard Boussinesq approximation in the natural convection of the buoyancy-driven flow and…
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
We propose an extension of quasi-Newton methods, and investigate the convergence and the robustness properties of the proposed update formulae for the approximate Hessian matrix. Fletcher has studied a variational problem which derives the…