Related papers: Gaussian Process Quadrature Moment Transform
The Method of Moments [Pea94] is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments. However, in practice and especially…
Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
The theory and computational methods for custom-made Gauss quadrature have been described in Gautschi's 2004 monograph. Gautschi has also provided Fortran and MATLAB code for the implementation and illustration of these methods. We have…
Exact calculation and even multiplicative error estimation of matrix permanent are challenging for both classical and quantum computers. Regarding the permanents of random Gaussian matrices, the additive error estimation is closely linked…
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…
Individual random trajectories of stochastic processes are often analyzed by using quadratic forms such as time averaged (TA) mean square displacement (MSD) or velocity auto-correlation function (VACF). The appropriate quadratic form is…
In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
We present an efficient method for evaluating random phase errors in phase shifters within photonic integrated circuits, avoiding the computational cost of traditional Monte Carlo simulations. By modeling spatially correlated manufacturing…
Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian…
The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF. The classical quadrature rules used in…
Computer experiments involving both qualitative and quantitative (QQ) factors have attracted increasing attention. Gaussian process (GP) models have proven effective in this context by choosing specialized covariance functions for QQ…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…