arXiv research

Post-process Bayesian inference speeds up posterior approximation.

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

Parallelized Bayesian quadrature improves sample efficiency and inference.

Bayesian quadrature uses probabilistic models for estimating intractable integrals.

Unified quadrature framework for large-scale kernel machines.

SOBER optimizes and quadrates efficiently in parallel for diverse tasks.

This work introduces a fixed-point optimization for variational inference.

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…

Novel approach for estimating conditional expectations using Bayesian quadrature.

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…

Bayesian quadrature improves conformal prediction for better risk assessment.

DBQPG improves policy gradient estimation with fewer samples.

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

Paper proposes efficient AL algorithms for optimizing product performance under environmental variability.

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

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

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…

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…

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

Adaptive quadrature improves Bayesian inference through active learning.

Paper develops efficient variational inference for sparse deep learning with theoretical guarantees.

Bayesian quadrature improves integration on Riemannian manifolds.

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…

Improved variational inference for logistic regression and classification.

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…

Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to the gradient or a large number of likelihood evaluations. We introduce here a n…

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 …

SOBER framework optimizes Bayesian optimization tasks efficiently.

The paper studies estimating the normalizing constant using queries to a black-box function in RKHS.

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…

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…

An exciting branch of machine learning research focuses on methods for learning, optimizing, and integrating unknown functions that are difficult or costly to evaluate. A popular Bayesian approach to this problem uses a Gaussian process (GP) to construct a posterior distribution over the function of interest given a se…

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…

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

New method for hyperparameter tuning in sparse matrix factorization.

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…

SSVI efficiently trains sparse Bayesian neural networks with minimal compression and performance loss.

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 …

While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that exploit the sparse spectral representation of a GP kernel. This paper presents such a…

Bayesian neural networks speed up numerical integration.

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Previous research has shown that BQ offers sample effic…

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 …

Paper introduces variational inference for Bayesian inverse problems with gamma hyperpriors.

Proposes a Bayesian approach for automatic node selection in sparse neural networks.

The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.

Improved VB algorithm for high-dimensional logistic regression with theoretical guarantees.