Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is the estimation of the graphon function that parametrizes the nonparametric exchangeable random graph model. Existing methods typically suffer from either limited accuracy or high computational complexity. We introduce a new histogram-based estimator with low algorithmic complexity that achieves high accuracy by jointly aligning the nodes of all graphs, in contrast to most conventional methods that order nodes graph by graph. Consistency results of the proposed graphon estimator are established. A numerical study shows that the proposed estimator outperforms existing methods in terms of accuracy, especially when the dataset comprises only small and variable-size networks. Moreover, the computing time of the new method is considerably shorter than that of other consistent methodologies. Additionally, when applied to a graph neural network classification task, the proposed estimator enables more effective data augmentation, yielding improved performance across diverse real-world datasets.

We study best-arm identification in stochastic dueling bandits under the sole assumption that a Condorcet winner exists, i.e., an arm that wins each noisy pairwise comparison with probability at least $1/2$. We introduce a new identification procedure that exploits the full gap matrix $Δ_{i,j}=q_{i,j}-\tfrac12$ (where $q_{i,j}$ is the probability that arm $i$ beats arm $j$), rather than only the gaps between the Condorcet winner and the other arms. We derive high-probability, instance-dependent sample-complexity guarantees that (up to logarithmic factors) improve the best known ones by leveraging informative comparisons beyond those involving the winner. We complement these results with new lower bounds which, to our knowledge, are the first for Condorcet-winner identification in stochastic dueling bandits. Our lower-bound analysis isolates the intrinsic cost of locating informative entries in the gap matrix and estimating them to the required confidence, establishing the optimality of our non-asymptotic bounds. Overall, our results reveal new regimes and trade-offs in the sample complexity that are not captured by asymptotic analyses based only on the expected budget.

Your Out-of-Distribution Detection Method is Not Robust!

Could Iran be using China's BeiDou system? Drone strike hits Al-Rasheed hotel in Baghdad's Green Zone near US embassy, no casualties reported A prominent hotel in central Baghdad's heavily fortified Green Zone was struck by a drone, amid reports that Iraqi air defences intercepted an attack over the United States Embassy. The strike on Monday evening hit the top floor of Al-Rasheed Hotel, causing damage but no casualties, according to two Iraqi security officials cited by The Associated Press (AP) news agency. Security sources told the Reuters news agency that two Katyusha rockets had been intercepted that evening near the US Embassy in the Green Zone, which houses diplomatic missions as well as international institutions and government offices. Earlier Monday, the Iran-backed Kataib Hezbollah announced that Abu Ali Al-Askari, a prominent security official with the paramilitary group, had been killed, without giving details on the circumstances.

Trump announces White House Chief of Staff Susie Wiles diagnosed with'early stage' breast cancer Trump's billionaire adviser publicly rebukes Iran war as JD Vance camp erupts over Israel nuke threat Kristi Noem referred for criminal investigation after'lying under oath' about $220M vanity scheme You don't have to fly to Turkey or Thailand... and can do it on your lunch break! Diet that cures pain and inflammation, devised by experts: Constant sickness and aching joints are the first signs of problems that left unchecked can turn deadly. Timothee Chalamet and Kylie Jenner's strained Oscars chat decoded by lip-reader as he gets snubbed and mocked The snubbed A-lister, drunken pics and C-List stars who plagued the most'exclusive' party: All the Oscars gossip Hollywood didn't want you to see at very messy afterparty Proof Leonardo DiCaprio sent a CLONE to the Oscars... alarming truth about Teyana Taylor's blow up... and a very dirty Barbra Streisand rumor: KENNEDY's most brutal review yet NYC's smiling socialist mayor is VERY different behind the scenes, as progressives who crossed him allege tyrannical and ruthless behavior Awful Timothee Chalamet's ego is bigger than Kylie's inflated butt... but it's so clear what's really going on here. Trump stunned by lurid rumor about Iran's new'gay' ayatollah Chilling new details of dismembered Emily Pike's final hours after she was snatched in Arizona desert and man detectives now believe murdered her'It's like he was possessed': Terrifying moment Alexander brother turned into a'monster' and raped me... and the four chilling words he said after horror attack - alleged victim claims After Oscars 2026, the whispered fear among Hollywood doctors is now massive... this is so much bigger than Ozempic. A-list stars ditch formal Oscars red carpet dresses for sexy party looks - with Jeff Goldblum's wife Emilie Livingston, Heidi Klum, Amelia Gray Hamlin and Kate Hudson turning up the heat at Vanity Fair bash Shock as man begs for death penalty for HIMSELF after pinning dead pastor's hands to wall and targeting other religious leaders How Oscars 2026 proved Hollywood has overdosed on Ozempic: Leading doctors name stars now at'extreme' risk... and reveal terrifying new side effects Billionaire Peter Thiel holds secret'Antichrist' meetings on the Vatican's doorstep READ MORE: Catholic priest warns'the stage is set' for the rise of the Antichrist US billionaire Peter Thiel is hosting a series of closed-door lectures in Rome on the doorstep of the Vatican, focused on the concept of the Antichrist.

Hundreds of passengers flying to Dubai spent 11 hours on a flight to nowhere after their plane was turned back over Egypt. The Emirates flight EK24 set off from Edinburgh at 21:26 on Sunday and was due to land in Dubai at 06:49 on Monday. However, as the plane flew over Egypt, flights at Dubai International Airport were suspended following a fire caused by an Iranian drone hitting a fuel tank. The plane was forced to return to Edinburgh. Travel journalist Simon Calder told the BBC's Radio Scotland Breakfast programme that although Dubai was on the UK Foreign Office's No go list, many people were still taking the risk of flying there. No injuries were reported following the drone strike but officials said they had taken all necessary measures to ensure public safety.

Timothee Chalamet and Kylie Jenner's strained Oscars chat decoded by lip-reader as he gets snubbed and mocked Timothee Chalamet, Oscars laughing stock: All the brutal digs aimed at star after he missed out on Best Actor and'looked like he wanted to cry' A-list stars ditch formal Oscars red carpet dresses for sexy party looks - with Jeff Goldblum's wife Emilie Livingston, Heidi Klum, Amelia Gray Hamlin and Kate Hudson turning up the heat at Vanity Fair bash Teyana Taylor erupts backstage at Oscars after being'shoved' How Oscars 2026 proved Hollywood has overdosed on Ozempic: Leading doctors name stars now at'extreme' risk... and reveal terrifying new side effects Trump stunned by lurid rumor about Iran's new'gay' ayatollah Awful Timothee Chalamet's ego is bigger than Kylie's inflated butt... but it's so clear what's really going on here. You don't have to fly to Turkey or Thailand... and can do it on your lunch break! Chilling US secrets of Iran leader who chants'Death to America'... including daughter who got a green card under Biden Israel blows up Ayatollah Khamenei's personal jet amid claims his injured heir Mojtaba'has been flown to Moscow for treatment' NYC's smiling socialist mayor is VERY different behind the scenes, as progressives who crossed him allege tyrannical and ruthless behavior Menopause made me put on 3 stone and I didn't recognise myself in photos. Here's the exact regime that helped me lose the weight - along with my brain fog and anxiety Pentagon officials have nicknamed his interfering wife'Yoko Ono'. But can she save Trump's bloodthirsty War Secretary Pete Hegseth from being thrown to the wolves? asks TOM LEONARD Chilling new details of dismembered Emily Pike's final hours after she was snatched in Arizona desert and man detectives now believe murdered her Monster'Triple-Threat' megastorm threatens 200 million across the US with travel chaos and power outages Kim Kardashian struggles to WALK in skintight golden gown and towering'stripper heels' as she attends the Vanity Fair Oscars party READ MORE: Watch as China's humanoids perform a Kung Fu display In what sounds like a scene from a science fiction thriller, a humanoid robot has been arrested by police after terrifying an elderly woman in China .

Iraq's Prime Minister Mohammed Shia al-Sudani faces pressure to act against Iran-backed terrorist groups following increased attacks on U.S., European, and Kurdish assets in the country.

They don't cope well in certain situations and the'transparent' mode lets in unwanted noise

President Donald Trump warns NATO allies they face a 'very bad' future if they don't help defend the Strait of Hormuz, telling The Financial Times beneficiaries should assist.