Related papers: Filtering of Gaussian processes in Hilbert spaces
We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…
Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the…
The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
In a variety of problems, the number and state of multiple moving targets are unknown and are subject to be inferred from their measurements obtained by a sensor with limited sensing ability. This type of problems is raised in a variety of…
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately…
An efficient algorithm for computing lower bounds on the global linear complexity of nonlinearly filtered PN-sequences is presented. The technique here developed is based exclusively on the realization of bit wise logic operations, which…
Variable selection is a widely studied problem in high dimensional statistics, primarily since estimating the precise relationship between the covariates and the response is of great importance in many scientific disciplines. However, most…
Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincar\'e inequalities to bound the Wasserstein distance between the true joint distribution of the prediction…
The extraction of spectral densities from Euclidean correlators evaluated on the lattice is an important problem, as these quantities encode physical information on scattering amplitudes, finite-volume spectra, inclusive decay rates, and…
It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…
Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic…
Generative diffusion models and many stochastic models in science and engineering naturally live in infinite dimensions before discretisation. To incorporate observed data for statistical and learning tasks, one needs to condition on…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…
Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…