Trump says he's'not afraid' of Vietnam-style ground combat in Iran Furious US troops erupt at CNN's $20m steak and lobster claims as grim photos expose reality Hollywood's top insider makes VERY catty observation about Kaitlan Collins Pam Bondi is formally subpoenaed by Congress as Trump's Epstein nightmare grows What the Jane Plan did to my body: The unfashionable retro diet's fans say it's life-changing, easy, better than fat jabs - and shifts weight fast. My husband tried a'cure' for his ALS... days later he went blind and couldn't move. The children screamed on video call as he died. Outrage after Pete Hegseth aide ousted for'leaks' lands new top secret intelligence job Everything JFK Jr told friends about his love affair with'sexual dynamo' Madonna... her unprintable pillow talk... and his perverse incest request that she couldn't go through with SARAH VINE: How telling that Meghan's joined the ranks of those peddling wellness and fake lifestyles to the gullible My chilling conversations with the Unabomber and America's worst serial killers when I ran a Supermax prison, revealed in The Crime Desk newsletter Oscars afterparty snitches reveal cringing details of how stars stopped talking to him... a brutal message from Kylie's gloating ex... and her'humiliating' admission to friends Joe Burrow cements his place as the NFL's most eligible bachelor as he is spotted cozying up to Tate McRae and Alix Earle at glitzy Oscars afterparty Dark secret past of husband killer Kouri Richins' Iraq war veteran lover revealed... and their toe-curling sex texts that helped convict her Mystery as Communion bread and wine'miraculously' appear to turn into human tissue and blood READ MORE: Scientists stunned as 500-year-old'miracle' image of Virgin Mary reveals impossible microscopic reflection Catholics believe that during Communion, bread and wine become the body and blood of Jesus Christ, though they continue to appear unchanged to the human eye. But there have been a handful of rare and debated cases in which the sacred elements appeared to take on a far more literal, physical form.

Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape. On the other hand, gradient descent with perturbations [Ge et al., 2015, Jin et al., 2017] is not slowed down by saddle points--it can find an approximate local minimizer in polynomial time. This result implies that GD is inherently slower than perturbed GD, and justifies the importance of adding perturbations for efficient non-convex optimization. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

We propose an alternative framework to existing setups for controlling false alarms when multiple A/B tests are run over time. This setup arises in many practical applications, e.g. when pharmaceutical companies test new treatment options against control pills for different diseases, or when internet companies test their default webpages versus various alternatives over time. Our framework proposes to replace a sequence of A/B tests by a sequence of best-arm MAB instances, which can be continuously monitored by the data scientist. When interleaving the MAB tests with an online false discovery rate (FDR) algorithm, we can obtain the best of both worlds: low sample complexity and any time online FDR control. Our main contributions are: (i) to propose reasonable definitions of a null hypothesis for MAB instances; (ii) to demonstrate how one can derive an always-valid sequential p-value that allows continuous monitoring of each MAB test; and (iii) to show that using rejection thresholds of online-FDR algorithms as the confidence levels for the MAB algorithms results in both sample-optimality, high power and low FDR at any point in time. We run extensive simulations to verify our claims, and also report results on real data collected from the New Yorker Cartoon Caption contest.

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How the US left Ukraine exposed to Russia's winter war Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? Starmer, Zelenskyy urge'focus' on Ukraine as Iran war diverts attention Ukrainian President Volodymyr Zelenskyy has met British Prime Minister Keir Starmer in London to sign a new defence pact as the unfolding US-Israeli war on Iran threatened to divert international attention away from Russia's attacks on Ukraine. Starmer welcomed Zelenskyy at his official Downing Street residence on Tuesday, reassuring the Ukrainian leader that "the focus must remain on Ukraine", days after the US partially rolled back sanctions against Moscow to cool oil prices sent soaring by its attacks on Iran. "There is obviously a conflict in Iran going on, in the Middle East, but we can't lose focus on what's going on in Ukraine and the need for our support there," said Starmer, who was meeting Zelenskyy to sign a defence partnership aimed at boosting "global defensive capability against the proliferation of low-cost, high-tech military hardware".

Many online platforms act as intermediaries between a seller and a set of buyers. Examples of such settings include online retailers (such as Ebay) selling items on behalf of sellers to buyers, or advertising exchanges (such as AdX) selling pageviews on behalf of publishers to advertisers. In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixed-percentage revenue sharing schemes are often used to split the revenue among the platform and the sellers. In particular, such revenue sharing schemes require the platform to (i) take at most a constant fraction \alpha of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold. A straightforward way to satisfy the constraints is to set a reserve price at c / (1 - \alpha) for each item, but it is not the optimal solution on maximizing the profit of the intermediary.

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the trace of the conditional covariance operator. We prove various consistency results for this procedure, and also demonstrate that our method compares favorably with other state-of-the-art algorithms on a variety of synthetic and real data sets.

The BBC has obtained footage and interviews from the Iranian capital Tehran which evoke a city of strained nerves, of constant waiting for the next air strike and relentless fear of the state security apparatus. The identities of the people in this report have been protected. While independent journalists still try to gather testimony that offers a credible alternative view, they run the risk of arrest, torture and possibly worse. Displaced Palestinians were told to secure their tents to prevent them being blown away as a storm swept through the enclave. Video filmed by a witness and verified by the BBC shows a drone crashing close to the airport.

Dyson's Newest Wet Floor Cleaner Is Available as of Today The debut follows the release of Dyson's newest robot vacuum and larger wet cleaner last week. Welcome to a new world of mopping options from Dyson. After announcing several new models last year at IFA Berlin, Dyson has begun rolling out its latest suite of vacuums and wet floor cleaners to the public. Last week, Dyson's newest robot vacuum, the Spot+Scrub Ai ($1,200), became available for purchase online, along with the Clean+Wash Hygiene ($500), one of the brand's new wet floor cleaners. The recently announced Dyson PencilWash ($350) is available as of today.

The paper addresses the classical network tomography problem of inferring local traffic given origin-destination observations. Focussing on large complex public transportation systems, we build a scalable model that exploits input-output information to estimate the unobserved link/station loads and the users path preferences. Based on the reconstruction of the users' travel time distribution, the model is flexible enough to capture possible different path-choice strategies and correlations between users travelling on similar paths at similar times. The corresponding likelihood function is intractable for medium or large-scale networks and we propose two distinct strategies, namely the exact maximum-likelihood inference of an approximate but tractable model and the variational inference of the original intractable model. As an application of our approach, we consider the emblematic case of the London Underground network, where a tap-in/tap-out system tracks the start/exit time and location of all journeys in a day. A set of synthetic simulations and real data provided by Transport For London are used to validate and test the model on the predictions of observable and unobservable quantities.