Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$¥sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high dimensional. These rules are based on the assumption that the integrand has a certain degree of smoothness, which is expressed as that the integrand belongs to a certain reproducing kernel Hilbert space (RKHS). However, this assumption can be violated in practice (e.g., when the integrand is a black box function), and no general theory has been established for the convergence of kernel quadratures in such misspecified settings. Our contribution is in proving that kernel quadratures can be consistent even when the integrand does not belong to the assumed RKHS, i.e., when the integrand is less smooth than assumed. Specifically, we derive convergence rates that depend on the (unknown) lesser smoothness of the integrand, where the degree of smoothness is expressed via powers of RKHSs or via Sobolev spaces.

PCWorld reports Microsoft's Copilot Health is a new AI tool that organizes personal medical data from wearables like Apple Watch and hospital records. Currently available in the U.S. for users 18+ via waitlist, it aims to help prepare for doctor visits while emphasizing it's not a doctor replacement. The tool features encrypted, isolated data storage with user control, though concerns exist about AI accuracy in medical advice per Nature Medicine studies. Ready to let AI pore over your medical records? Claude and ChatGPT are already doing it, and now Microsoft's Copilot is ready to review your chart.

Deep neural networks, and in particular recurrent networks, are promising candidates to control autonomous agents that interact in real-time with the physical world. However, this requires a seamless integration of temporal features into the network's architecture. For the training of and inference with recurrent neural networks, they are usually rolled out over time, and different rollouts exist.

Thank you for joining us on the Enterprise AI hub. In this episode of the Infosys Knowledge Institute Podcast, Dylan Cosper speaks with Sriram Kalyan, head of applications and data at Nutrien Ag Solutions, Australia, about turning a high-risk post-acquisition IT landscape into a scalable digital foundation. Sriram shares how the merger of two major Australian agricultural companies created duplicated systems, fragile integrations, and operational risk, compounded by the sudden loss of key platform experts and partners. He explains how leadership alignment, disciplined platform consolidation, and a clear focus on business outcomes transformed integration from an invisible liability into a strategic enabler, positioning Nutrien Ag Solutions for future growth, cloud transformation, and enterprise scale. A "QuitGPT" campaign is urging people to cancel their ChatGPT subscriptions Michelle Kim Here are our picks for the advances to watch in the years ahead--and why we think they matter right now. A "QuitGPT" campaign is urging people to cancel their ChatGPT subscriptions Backlash against ICE is fueling a broader movement against AI companies' ties to President Trump.

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.