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We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

High precision measurements are essential to solve major scientific and technological challenges, from gravitational wave detection to healthcare diagnostics. Quantum sensing delivers greater precision, but an in-depth optimisation of…

In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…

We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose…

When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…

Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…

Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…

The advancement and scaling of quantum technology has made the learning and identification of quantum systems and devices in highly-multidimensional parameter spaces a pressing task for a variety of applications. In many cases, the…

We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…

We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy…

Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…

Quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this paper, we propose a Bayesian quantile trend filtering…

Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…