Related papers: A probabilistic approach to direction-dependent io…

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

Let $P$ be a linear differential operator over $\mathcal{D} \subset \mathbb{R}^d$ and $U = (U_x)_{x \in \mathcal{D}}$ a second order stochastic process. In the first part of this article, we prove a new necessary and sufficient condition…

Many applications of classification methods not only require high accuracy but also reliable estimation of predictive uncertainty. However, while many current classification frameworks, in particular deep neural networks, achieve high…

We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…

We investigate interferometric techniques to estimate the deflection angle of an optical beam and compare them to the direct detection of the beam deflection. We show that quantum metrology methods lead to a unifying treatment for both…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach due to the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Systematic effects that limit the achievable sensitivity of current low-frequency radio telescopes to the 21 cm signal are among the foremost challenges in observational 21 cm cosmology. The standard approach to retrieving the 21 cm signal…

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…

Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…

This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…

Perception is one of the key abilities of autonomous mobile robotic systems, which often relies on fusion of heterogeneous sensors. Although this heterogeneity presents a challenge for sensor calibration, it is also the main prospect for…

The detection of periodic signals in irregularly-sampled time series is a problem commonly encountered in astronomy. Traditional tools used for periodic searches, such as the periodogram, have poorly defined statistical properties under…

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…

We investigate the estimation of dephasing-induced decoherence in continuous-variable quantum systems using non-Gaussian probe states. By purifying the open system, we identify optimal probes, specifically squeezed cat and symmetric…

Calibrating out per-antenna signal chain effects is an essential step in analyzing radio interferometric data. For drift-scanning arrays, robustly calibrating the data is especially challenging due to the lack of the ability to track a…