A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
SOBER optimizes and quadrates efficiently in parallel for diverse tasks.
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…
Parallelized Bayesian quadrature improves sample efficiency and inference.
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.
Bayesian Quadrature improves ensembling for neural networks with dispersed likelihood peaks.
BayesSum improves Bayesian quadrature for discrete domains, requiring fewer samples.
Post-process Bayesian inference speeds up posterior approximation.
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.
Bayesian quadrature improves integration on Riemannian manifolds.
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…
Combines control variates and adaptive importance sampling for Monte Carlo integration.
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…
Paper proposes a new estimator for nested expectations with faster convergence.
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…
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 …
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…
Bayesian Probabilistic Integration uses BART for high-dimensional, non-smooth functions.
Paper proposes efficient AL algorithms for optimizing product performance under environmental variability.
Improves Bayesian optimization for multi-fidelity functions.
Bayesian quadrature optimization (BQO) maximizes the expectation of an expensive black-box integrand taken over a known probability distribution. In this work, we study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A stan…
New methods for Bayesian inference using mean shift particle systems.
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to incomplete/finite information about the continuous mathematical problem being approxi…
TQ separates sampling and integration for high-dimensional integrals.
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of methods that are 'well-calibrated' in a specific sense. But the computational c…
Adaptive batch sizes improve active learning efficiency and flexibility.
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 , where and encode the smoothness and dimension of the integrand. However, an empirical investigation re…
This paper provides a dictionary of closed-form kernel mean embeddings.
This work introduces a fixed-point optimization for variational inference.
We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in probabilistic inference is numerical integration, to average over ensembles of models or unk…
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
The paper analyzes greedy algorithms for MMD minimization, showing their efficiency and approximation error.
Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.