Patriot missile involved in Bahrain blast likely U.S.-operated, analysis finds Smoke rises following a strike on the Bapco Oil Refinery, amid the U.S.-Israeli conflict with Iran, on Sitra Island Bahrain, on March 9. | REUTERS An American-operated Patriot air defense battery likely fired the interceptor missile involved in a pre-dawn explosion that injured dozens of civilians and tore through homes in U.S.-ally Bahrain 10 days into the war on Iran, according to an analysis by academic researchers examined by Reuters. Both Bahrain and Washington have blamed an Iranian drone attack for the March 9 blast, which the Gulf kingdom said injured 32 people including children, some seriously. Commenting on the day of the attack, U.S. Central Command said on X that an Iranian drone struck a residential neighborhood in Bahrain. In response to questions, Bahrain on Saturday acknowledged for the first time that a Patriot missile was involved in the explosion over the Mahazza neighborhood on Sitra island, offshore from the capital Manama and also home to an oil refinery. In a statement, a Bahraini government spokesperson said the missile successfully intercepted an Iranian drone mid-air, saving lives. In a time of both misinformation and too much information, quality journalism is more crucial than ever.

We investigate the statistical performance and computational efficiency of the alternating minimization procedure for nonparametric tensor learning. Tensor modeling has been widely used for capturing the higher order relations between multimodal data sources. In addition to a linear model, a nonlinear tensor model has been received much attention recently because of its high flexibility. We consider an alternating minimization procedure for a general nonlinear model where the true function consists of components in a reproducing kernel Hilbert space (RKHS). In this paper, we show that the alternating minimization method achieves linear convergence as an optimization algorithm and that the generalization error of the resultant estimator yields the minimax optimality. We apply our algorithm to some multitask learning problems and show that the method actually shows favorable performances.

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.

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.

Antibodies are crucial proteins produced by the immune system to eliminate harmful foreign substances and have become pivotal therapeutic agents for treating human diseases.

Such a phenomenon is illustrated in Figure 1 where the learned predictive function from the source data may significantly differ from the true function.