Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super 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.

This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG .

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Air strikes have targeted the headquarters of the Iran-aligned Popular Mobilisation Forces (PMF) in Iraq's capital, Baghdad, as the country becomes a two-way battlefield between armed factions and the United States during its war with Iran . The US carried out strikes against the Shia paramilitary umbrella group, also known locally as Hashed al-Shaabi, late on Sunday after attacks on a US diplomatic and logistics centre at Baghdad International Airport. The attack was carried out after Iraqi security officials said four explosions were heard near Camp Victory, a US logistics centre at the capital's main airport. Al Jazeera's Assed Baig, reporting from Baghdad, said some drones "breached air defences and caused damage, more symbolic damage than anything else". "At the same time, Iraqi security forces have set up checkpoints around Baghdad to try and stop these drone strikes because some of these factions are launching drones from the vicinity of Baghdad," he said.

While neural machine translation (NMT) is making good progress in the past two years, tens of millions of bilingual sentence pairs are needed for its training. However, human labeling is very costly. To tackle this training data bottleneck, we develop a dual-learning mechanism, which can enable an NMT system to automatically learn from unlabeled data through a dual-learning game. This mechanism is inspired by the following observation: any machine translation task has a dual task, e.g., English-to-French translation (primal) versus French-to-English translation (dual); the primal and dual tasks can form a closed loop, and generate informative feedback signals to train the translation models, even if without the involvement of a human labeler. In the dual-learning mechanism, we use one agent to represent the model for the primal task and the other agent to represent the model for the dual task, then ask them to teach each other through a reinforcement learning process. Based on the feedback signals generated during this process (e.g., the languagemodel likelihood of the output of a model, and the reconstruction error of the original sentence after the primal and dual translations), we can iteratively update the two models until convergence (e.g., using the policy gradient methods). We call the corresponding approach to neural machine translation dual-NMT. Experiments show that dual-NMT works very well on English French translation; especially, by learning from monolingual data (with 10% bilingual data for warm start), it achieves a comparable accuracy to NMT trained from the full bilingual data for the French-to-English translation task.

In a place denied access to basic forensic technology--and where people disappear into Israeli detention--the fate of thousands remains unknown. One of them is an autistic teenager. In the early morning dark, Abeer Skaik turned to her husband, Ali Al-Qatta, and said that today would be the day they would find their son. Ali nodded in silence, and she handed him the stack of flyers. Each bore a photograph of 16-year-old Hassan smiling widely, his shoulders loose, wearing a plain red T-shirt. He is looking directly at the camera, unguarded. On top of the page, in large letters, Abeer had written a single word in bold red ink: --an appeal. Abeer watched as Ali stepped into a car with a few close friends and drove away. They started the 30-kilometer trip south, from al-Tuffah, east of Gaza City, to the European Hospital in Khan Younis. They had heard that a group of people detained by Israel, including children, would be released there. The gate was already crowded. Families stood shoulder to shoulder, wrapped in blankets against the cold, clutching photographs and ID cards. Ali distributed the flyers among his friends. When the buses of released detainees arrived, he and the others moved slowly through the narrow gaps between clusters of people. Some of those who had just been released were being pulled into embraces. Ali waited at the edge of each reunion. "Have you seen my son?" he asked. One after another, people shook their heads.

Don't Listen to Anyone Who Thinks Secession Will Solve Anything Americans increasingly fantasize about a divorce between red and blue states--but they dread the thought of civil war. You can't have one without the other. It's become almost like a histamine response: After a shocking national event like the assassination of Charlie Kirk, or Donald Trump's deployment of the military to Los Angeles last June, mentions of the term " civil war " and calls for secession surge online. This kind of talk flared again in January, when two citizens were shot and killed by immigration agents on the streets of Minneapolis, and governor Tim Walz mobilized the Minnesota National Guard to be ready to support local law enforcement. "I mean, is this a Fort Sumter?" Walz said in an interview with The Atlantic, invoking the battle that sparked the Civil War.