Related papers: Gaussian Measures Conditioned on Nonlinear Observa…
In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of…
We propose a modeling framework for stochastic systems, termed Gaussian behaviors, that describes finite-length trajectories of a system as a Gaussian process. The proposed model naturally quantifies the uncertainty in the trajectories, yet…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
A methodology is developed to extract $d$ invariant features $W=f(X)$ that predict a response variable $Y$ without being confounded by variables $Z$ that may influence both $X$ and $Y$. The methodology's main ingredient is the penalization…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
Model Predictive Control evolved as the state of the art paradigm for safety critical control tasks. Control-as-Inference approaches thereof model the constrained optimization problem as a probabilistic inference problem. The constraints…
We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…
We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown $d$-dimensional parameter, which might be subject to Gaussian random noises. They aim to…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…