Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and comprehensive treatment has been published. The purpose of this survey is to fill this gap. We review the mathematical foundations of Bayesian quadrature from different points of view; present a systematic taxonomy for classifying different Bayesian quadrature methods along the three axes of modelling, inference, and sampling; collect general theoretical guarantees; and provide a controlled numerical study that explores and illustrates the effect of different choices along the axes of the taxonomy. We also provide a realistic assessment of practical challenges and limitations to application of Bayesian quadrature methods and include an up-to-date and nearly exhaustive bibliography that covers not only machine learning and statistics literature but all areas of mathematics and engineering in which Bayesian quadrature or equivalent methods have seen use.

Modern machine learning systems are able to learn extremely complicated relations from data.

T o this end, we propose a simple yet powerful paradigm for seamlessly unifying different human pose and shape-related tasks and datasets. Our formulation is centered on the ability - both at training and test time - to query any arbitrary point of the human volume, and obtain its estimated location in 3D. We achieve this by learning a continuous neural field of body point localizer functions, each of which is a differently parameterized 3D heatmap-based convolutional point localizer (detector).

Recurrent neural networks (RNNs) notoriously struggle to learn long-term memories, primarily due to vanishing and exploding gradients.

Motion is a powerful cue that humans use to detect and segment visual objects.

However, practical model deployment often operates in the gap between these two limit cases, as real-world applications demand adaptation to specific subdomains, tasks or concepts -- spread over the entire, varying life cycle of a model.

Randomized smoothing is a popular certified defense against adversarial attacks.

We study causal effect estimation in a setting where the data are not i.i.d.