Arising from many applications at the intersection of decision-making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) problems unify the two main classes of inference, namely maximization (optimization) and marginal inference (counting), and are believed to have higher complexity than both of them. We propose XOR MMAP provides a constant factor approximation to the Marginal MAP problem, by encoding it as a single optimization in a polynomial size of the original problem. We evaluate our approach in several machine learning and decision-making applications, and show that our approach outperforms several state-of-the-art Marginal MAP solvers.

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Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are relatively robust to random noise. In this paper, we propose to study a semi-random noise regime that generalizes both the random and worst-case noise regimes. We propose the first quantitative analysis of the robustness of nonlinear classifiers in this general noise regime. We establish precise theoretical bounds on the robustness of classifiers in this general regime, which depend on the curvature of the classifier's decision boundary. Our bounds confirm and quantify the empirical observations that classifiers satisfying curvature constraints are robust to random noise. Moreover, we quantify the robustness of classifiers in terms of the subspace dimension in the semi-random noise regime, and show that our bounds remarkably interpolate between the worst-case and random noise regimes. We perform experiments and show that the derived bounds provide very accurate estimates when applied to various state-of-the-art deep neural networks and datasets. This result suggests bounds on the curvature of the classifiers' decision boundaries that we support experimentally, and more generally offers important insights onto the geometry of high dimensional classification problems.

Services such as Google TV and Amazon's Fire TV have recommendation systems, as well as search functions, that may prioritise some content over others. Services such as Google TV and Amazon's Fire TV have recommendation systems, as well as search functions, that may prioritise some content over others. World's broadcasters urge EU to tighten rules for big tech in smart TV battle The world's largest broadcasters have pushed for the EU to enforce its toughest regulations against virtual TVs and smart assistants built by Google, Amazon, Apple and Samsung . The call came in a letter from the Association of Commercial Television and Video on Demand Services in Europe (ACT), whose members include Canal+, RTL, Mediaset, ITV, Paramount+, NBCUniversal, Walt Disney, Warner Bros Discovery, Sky and TF1 Groupe. The letter argues that big tech companies have growing control over the operating systems of smart TVs and voice assistants, allowing them to act as "gatekeepers" funnelling users towards some content and away from others.

Unfortunately, the notion is seriously flawed on two counts [8]. First, it doesn't ensure fairness.

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.

We consider the problem of finding the best arm in a stochastic Mutli-armed Bandit (MAB) game and propose a general framework based on verification that applies to multiple well-motivated generalizations of the classic MAB problem. In these generalizations, additional structure is known in advance, causing the task of verifying the optimality of a candidate to be easier than discovering the best arm. Our results are focused on the scenario where the failure probability $\delta$ must be very low; we essentially show that in this high confidence regime, identifying the best arm is as easy as the task of verification. We demonstrate the effectiveness of our framework by applying it, and improving the state-of-the art results in the problems of: Linear bandits, Dueling bandits with the Condorcet assumption, Copeland dueling bandits, Unimodal bandits and Graphical bandits.

Due to health and energy concerns, the California Legislature is considering bills to prohibit data centers from being exempted from the state's stringent environmental law and impose new tariffs on new major energy users that strain power supplies.

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.