Related papers: On identifiability and consistency of the nugget i…
The maximum likelihood estimate of the correlation parameter of a Gaussian process with and without of a nugget term is studied in the case of the analysis of deterministic models.
The performance of machine learning models often relies on large labeled datasets; however, data collected from diverse sources can contain label noise. Recent work has shown that, in noisy settings, there may exist a subset of the training…
We introduce parametrisation of that property of the available training dataset, that necessitates an inhomogeneous correlation structure for the function that is learnt as a model of the relationship between the pair of variables,…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space…
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…
State-space models are dynamical systems defined by a latent and an observed process. In ecology, stochastic state-space models in discrete time are most often used to describe the imperfectly observed dynamics of population sizes or animal…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
We study global fluctuations for singular values of $M$-fold products of several right-unitarily invariant $N \times N$ random matrix ensembles. As $N \to \infty$, we show the fluctuations of their height functions converge to an explicit…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic…
In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…
We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…