arXiv research

New quadrature method using randomly pivoted Cholesky outperforms existing techniques.

Bayesian quadrature uses probabilistic models for estimating intractable integrals.

SOBER optimizes and quadrates efficiently in parallel for diverse tasks.

This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We pr…

Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.

We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the qua…

Bayesian quadrature improves integration efficiency with invariant priors.

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Improved kernel quadrature with convex weights using subsampling.

A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds optimal values of function (value-nodes) and the corresponding weights. The Gaussi…

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 the sigma-point filters are motivated via polynomial approximation of the integ…

In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using…

Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its key ingredient is an acquisition function that changes as a function of previou…

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…

Unified quadrature framework for large-scale kernel machines.

This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.

Novel approach for estimating conditional expectations using Bayesian quadrature.

New Fourier features improve high-precision approximation in large-scale problems.

Improved Nyström approximation for kernel quadrature with theoretical guarantees.

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 …

Parallelized Bayesian quadrature improves sample efficiency and inference.

Adaptive quadrature improves Bayesian inference through active learning.

A new method calculates accurate SABR model option prices and deltas.

DBQPG improves policy gradient estimation with fewer samples.

Improved kernel herding algorithm for faster quadrature rule convergence.

Bayesian quadrature improves conformal prediction for better risk assessment.

Efficiently marginalizes over Gaussian Process kernels for better model flexibility and uncertainty.

The paper improves error bounds for Bayesian quadrature in noisy settings.

Bayesian Quadrature improves ensembling for neural networks with dispersed likelihood peaks.

We present a framework for accelerating a spectrum of machine learning algorithms that require computation of bilinear inverse forms $u^\top A^{-1}u$, where $A$ is a positive definite matrix and $u$ a given vector. Our framework is built on Gauss-type quadrature and easily scales to large, sparse matrices. Further, it …

Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of variational sampling (i.e., combining quadrature with variational approximation). Exper…

BayesSum improves Bayesian quadrature for discrete domains, requiring fewer samples.

Kernel quadrature improves CRPS estimation for probabilistic time-series forecasting.

A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.

Combines control variates and adaptive importance sampling for Monte Carlo integration.

Bayesian quadrature improves integration on Riemannian manifolds.

The paper introduces new methods for Asian option pricing using Laguerre quadrature.

Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic numerical integration technique that performs promisingly when compared to traditional…

Faster training of neural ODEs using Gauß-Legendre quadrature.

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…

Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$\sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high d…

Paper proposes a new estimator for nested expectations with faster convergence.

Positive weights improve kernel quadrature's accuracy.

Post-process Bayesian inference speeds up posterior approximation.

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the range of the function of interest, such as nonnegativity or boundedness. Although …

New filters improve radar target inference in complex scenarios.

Bayesian optimisation has been successfully applied to a variety of reinforcement learning problems. However, the traditional approach for learning optimal policies in simulators does not utilise the opportunity to improve learning by adjusting certain environment variables: state features that are unobservable and ran…