arXiv research

Paper evaluates squared-exponential covariance function for Gaussian processes with integral observations.

The paper integrates Gaussian processes into numerical integration schemes to improve accuracy and uncertainty quantification.

Integration of the form $\int_a^\infty {f(x)w(x)dx}$, where $w(x)$ is either $\sin (ω{\kern 1pt} x)$ or $\cos (ω{\kern 1pt} x)$, is widely encountered in many engineering and scientific applications, such as those involving Fourier or Laplace transforms. Often such integrals are approximated by a numerical integration…

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly dete…

The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable…

Corrects local error estimates for UBU integrator in SDEs, improving complexity guarantees.

There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. A…

Study investigates how errors in reinsurance parameters degrade optimal solutions.

Improved sigma-point filters reduce quadrature error bias.

Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …

Paper proposes a method to numerically approximate differential privacy guarantees using FFT.

Derives equations for systems with external forces using variational methods.

Efficiently approximates integrals using a subset of samples from a target distribution in RKHS.

New method finds points for approximating distributions faster.

Study on error rates for approximating rough volatility models.

An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation …

Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…

Probabilistic solvers improve stability for stiff systems.

Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.

Paper introduces cubature method for stochastic Volterra equations.

L-HNNs improve Bayesian inference efficiency by reducing gradient computation.

Paper proposes efficient method to calculate Fisher-Bingham distribution normalizing constant.

Combines normalizing flows and quasi-Monte Carlo for improved numerical integration.

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussia…

FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a …

L-HNNs improve Bayesian inference by reducing gradient requirements and improving ESS.

A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential operators, and covariance functions associated to latent functions. In the classica…

The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the smoothness and dimension of the integrand. However, an empirical investigation re…

Improved LOO cross-validation for function approximation.

This paper analyzes AJIVE for estimating shared subspace across multiple datasets, revealing its strengths and limitations.

New algorithm speeds up MCMC for complex distributions.

CNN improves medium-range temperature forecasts with limited resources.

Combines experimental and historical data for robust policy evaluation.

MEDIDA discovers model errors in chaotic systems using sparse regression and data assimilation.

Hybrid model improves weather forecasting accuracy.

Unified kernel framework extends to stochastic systems, improving numerical stability.

New method uses Coulomb gases for Monte Carlo integration with reduced errors.

Efficient methods accelerate diffusion model sampling.

New algorithm improves sampling efficiency for complex systems.

Develops AMITE for analyzing neural network nonlinearities.

In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by Wüthrich et a…

We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational parameters, the VH bound involves minimization of a convex upper bound to the intract…

GIT-Net uses neural networks to approximate PDE operators efficiently.

The paper improves probabilistic herding methods using Gibbs distributions.

Paper uses DNN-based MoM-GAN to estimate contaminated data distributions.

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) a…

A new meta-analysis model detects and accommodates outliers.