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Found 13 papers, 5 papers with code
Orthonormal Expansions for Translation-Invariant Kernels
We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$.
Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel.
Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation
We prove that the maximum likelihood estimate of the smoothness parameter cannot asymptotically undersmooth the truth when the data are obtained on a fixed bounded subset of $\mathbb{R}^d$.
ProbNum: Probabilistic Numerics in Python
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference.
Black Box Probabilistic Numerics
One approach is to model the unknown quantity of interest as a random variable, and to constrain this variable using data generated during the course of a traditional numerical method.
Small Sample Spaces for Gaussian Processes
It is known that the membership in a given reproducing kernel Hilbert space (RKHS) of the samples of a Gaussian process $X$ is controlled by a certain nuclear dominance condition.
A probabilistic Taylor expansion with Gaussian processes
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order.
Semi-Exact Control Functionals From Sard's Method
The numerical approximation of posterior expected quantities of interest is considered.
Computation Methodology
Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions
We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become "slowly" overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model.
Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an It\^{o} stochastic differential equation (SDE), and the measurements are obtained at discrete time instants.
Improved Calibration of Numerical Integration Error in Sigma-Point Filters
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.
Symmetry Exploits for Bayesian Cubature Methods
Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited.
Methodology Numerical Analysis Computation
Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise
Advantage of the Student- t process quadrature over the traditional Gaussian process quadrature, is that the integral variance depends also on the function values, allowing for a more robust modelling of the integration error.
