Related papers: Rolled Gaussian process models for curves on manif…
Establishing mathematical models is a ubiquitous and effective method to understand the objective world. Due to complex physiological structures and dynamic behaviors, mathematical representation of the human face is an especially…
Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve…
This paper is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly-symmetric stationary…
For a family of quasi-arithmetic means satisfying certain smoothness condition we majorize the speed of convergence of the iterative sequence of self-mappings having a mean on each entry, described in the definition of Gaussian product, to…
In this paper, we perform registration of noisy curves. We provide an appropriate model in estimating the rotation and scaling parameters to adjust a set of curves through a M-estimation procedure. We prove the consistency and the…
Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primarily focus on low dimensional constrained domains for heat…
We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…
A probabilistic machine learning model is introduced to augment the $k-\omega\ SST$ turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods…
In this paper, we consider two cases of rolling of one smooth connected complete Riemannian manifold $(M,g)$ onto another one $(\hM,\hg)$ of equal dimension $n\geq 2$. The rolling problem $(NS)$ corresponds to the situation where there is…
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. We focus on two applications involving the classification of mouse vertebrae shape…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
Graph Gaussian Processes (GGPs) provide a data-efficient solution on graph structured domains. Existing approaches have focused on static structures, whereas many real graph data represent a dynamic structure, limiting the applications of…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…
We compute the geodesic curvature of logarithmic spirals on surfaces of constant Gaussian curvature. In addition, we show that the asymptotic behavior of the geodesic curvature is independent of the curvature of the ambient surface. We also…
The paper covers the design and analysis of experiments to discriminate between two Gaussian process models, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered.…