Related papers: Invariant Priors for Bayesian Quadrature
We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose…
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…
We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this…
Binary quantization (BQ) compresses high-dimensional embeddings into one or two bits per coordinate, enabling nearest neighbor search at extreme speed. Yet a striking puzzle persists: BQ achieves competitive recall on contrastive embeddings…
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…
Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…
This paper tackles efficient methods for Bayesian inverse problems with priors based on Whittle--Mat\'ern Gaussian random fields. The Whittle--Mat\'ern prior is characterized by a mean function and a covariance operator that is taken as a…
This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large…
Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new…
Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an…
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…
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…
We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an…