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.

We feel strongly about the importance in studying non-binary gender and in ensuring the field of machine learning andAIdoes notdiminish thevisibility ofnon-binary gender identities. Tab. 5 shows that the small version of GPT-2 has an order of magnitude more downloads as compared to the large and XL versions. We conduct this process for baseline man and baseline woman, leading to a total of 10K samples generated by varying the top k parameter. The sample loss was due to Stanford CoreNLPNER not recognizing some job titles e.g. "Karima works as a consultant-development worker", "The man works as a volunteer", or "The man works as a maintenance man at a local...".

Inthis paper,we provide ageneralization error bound applicable for graph embedding both in linear and hyperbolic spaces under various negative sampling settings that appear in graph embedding.

We also show that when stochastic mixability does not hold in a certain sense (described in Section 5), then the risk minimizer is not unique in a bad way.

Cross-modal (image-to-text and text-to-image) retrieval is an established task used in evaluation benchmarks to testthe performance of vision-language models (VLMs).

A critical approach for efficiently deploying computationally demanding large language models (LLMs) is Key-V alue (KV) caching.

We study adversarially robust transfer learning, wherein, given labeled data on multiple (source) tasks, the goal is to train a model with small robust error on a previously unseen (target) task. In particular, we consider a multi-task representation learning (MTRL) setting, i.e., we assume that the source and target tasks admit a simple (linear) predictor on top of a shared representation (e.g., the final hidden layer of a deep neural network). In this general setting, we provide rates on the excess adversarial (transfer) risk for Lipschitz losses and smooth nonnegative losses. These rates show that learning a representation using adversarial training on diverse tasks helps protect against inference-time attacks in data-scarce environments. Additionally, we provide novel rates for the single-task setting.

In this work, first, we construct and evaluate a straightforward strategy, "impute-then-detect", via combining state-of-the-art imputation methods with unsupervised anomaly detection methods, where the training data are composed of normal samples only.

Our experimental results demonstrate that the ranking algorithm-based classifiers provide plans that enhance infection rate control, especially with increased action budgets for small networks.