Trump's stunning Georgia silence gifts America's'most endangered Democrat' Jon Ossoff a vital lifeline Ugly behind-the-scenes reality of Blake Lively's'paradise' compound: Unpaid workers, a $2MILLION debt... and humiliating new question she and Ryan Reynolds must now face Hidden warning signs you are taking the WRONG dose of Ozempic: Doctor sounds alarm over dangerous mistake... and reveals four lifestyle tweaks to avoid horror side effects'Beloved' college basketball player tragically killed in hit-and-run accident Inside Meryl Streep's very secret relationship with Martin Short: Friends finally reveal how pair bonded through trauma... incredible measures they take to hide the truth... and why there is'no doubt they are in love' Trumpworld's new eyebrow-raising addiction that even health boss RFK Jr admits to using daily Young American women in the crosshairs of dark network: They flirt and flatter, watching every move... then they strike The Chicks' Natalie Maines delivers foul-mouthed Trump rant 23 years after famously slamming George W. Bush Fast-food chain struggles under California's soaring minimum wage as frightened staff abandon crime-ridden locations Middle-aged male school board member faces criminal charges after flirting with teenage girl at public meeting: 'God, you're hot' Michelle Obama says same'anger' that led to husband's presidential victory is fueling Trump's MAGA movement: 'Those folks are drowning' Hero Amazon delivery driver jumps to woman's defense and saved her life during horror hammer attack at her home San Diego mosque shooters hated EVERYONE, according to manifesto being combed by FBI after massacre, as killer teen's $1m home is raided by cops Why Taylor Swift has cut out Travis Kelce's father ahead of wedding: He'cannot be trusted', say insiders... as'f***ed up' Blake Lively drama and preposterous demands leak out Spotify's 20th anniversary logo sparks a new'discomorphism' trend - here's how you can give ANY logo the disco ball treatment Spotify's disco ball logo has sparked a new trend online, which users are calling'discomorphism'. The logo was released to celebrate Spotify's 20th anniversary, and features a green, glittering disco ball. The change didn't go down well with many users - including one who called it the'biggest downgrade in history'. However, others were so inspired that they have created a new Discomorphism app . The app, which is the brainchild of Lovable, uses AI to give the disco ball treatment to any logo.

Trump's stunning Georgia silence gifts America's'most endangered Democrat' Jon Ossoff a vital lifeline Ugly behind-the-scenes reality of Blake Lively's'paradise' compound: Unpaid workers, a $2MILLION debt... and humiliating new question she and Ryan Reynolds must now face Hidden warning signs you are taking the WRONG dose of Ozempic: Doctor sounds alarm over dangerous mistake... and reveals four lifestyle tweaks to avoid horror side effects'Beloved' college basketball player tragically killed in hit-and-run accident Inside Meryl Streep's very secret relationship with Martin Short: Friends finally reveal how pair bonded through trauma... incredible measures they take to hide the truth... and why there is'no doubt they are in love' Trumpworld's new eyebrow-raising addiction that even health boss RFK Jr admits to using daily Young American women in the crosshairs of dark network: They flirt and flatter, watching every move... then they strike The Chicks' Natalie Maines delivers foul-mouthed Trump rant 23 years after famously slamming George W. Bush Fast-food chain struggles under California's soaring minimum wage as frightened staff abandon crime-ridden locations Middle-aged male school board member faces criminal charges after flirting with teenage girl at public meeting: 'God, you're hot' Michelle Obama says same'anger' that led to husband's presidential victory is fueling Trump's MAGA movement: 'Those folks are drowning' Hero Amazon delivery driver jumps to woman's defense and saved her life during horror hammer attack at her home San Diego mosque shooters hated EVERYONE, according to manifesto being combed by FBI after massacre, as killer teen's $1m home is raided by cops Why Taylor Swift has cut out Travis Kelce's father ahead of wedding: He'cannot be trusted', say insiders... as'f***ed up' Blake Lively drama and preposterous demands leak out An alien invasion might sound like science fiction, but a scientist has now revealed what the terrifying consequences of an encounter might be. Professor Avi Loeb, head of Harvard University's Galileo Project, claims our first encounter with an alien invader won't resemble sci-fi movies like E.T or War of the Worlds. Rather than a biological, flesh and blood alien, Professor Loeb explains that we are more likely to be met by a'technological device guided by AI '. The arrival of such a device would pose a'potential threat to all earthlings', he claims - sparking political, economic, and spiritual chaos around the world. Professor Loeb told the Daily Mail that'the stock market may crash due to the uncertainty about the impact of the encounter on the future of humanity.'

Hannah Jeter makes rare public appearance and still fires heat, Shania Twain's new look stuns & HOA Karen! 'Yellowstone' fans go absolutely wild for Taylor Sheridan's new spinoff, ratings soar Chiefs heiress Gracie Hunt might have set a bridesmaids record, fighting in the Dover parking lot & wings! Nothing to see here: Cowboys quarterback Dak Prescott and his ex's bridesmaid are just friends Can't sleep, Japanese bear-fighting robo-wolves will eat me and a gorilla trade captivates the nation A replica of KITT from'Knight Rider' got a traffic ticket in another state despite being in a museum Jena Sims covers her butt with a bow at the SI Swimsuit party, the NFL saves us from Romo & is Star Wars dead? Taylor Sheridan shocks'Yellowstone' fans with new spinoff series, provides viewers with dark ride Early reviews for new'Star Wars' movie are generally horrific, but does anyone even care at this point? Trump says Iran knows what's going to happen soon as military options weighed Shooting at Islamic center of San Diego'active but contained,' police say South Carolina AG calls out Murdaugh attorney's'bald-faced allegations' after civil rights suit Trump-backed Gallrein blasts Massie as'misrepresentative,' defends record ahead of Kentucky primary Barstool founder Dave Portnoy blasted the WNBA's latest marketing move as the most idiotic promo in sports history, and Dan Dakich is jumping into the fray. Watch as Dan reacts to Portnoy's viral rant before delivering his own unfiltered take on how the league is fumbling its biggest cash cow, Caitlin Clark.

It's an expensive time to fly. These tips can help lighten the load on your wallet. As a general rule, global instability leads to higher prices, and boy, is the world a doozy right now . Airfare hasn't escaped the tumult: US airfares are up 14.9 percent compared to a year ago, according to NerdWallet, largely due to fuel price spikes linked to disruptions in the Strait of Hormuz caused by blockages, bombs, and blockades. While the medium-term outlook for the airline business isn't great, there are still a few smart and tricky ways to save a little money when flying this summer.

Curt Cignetti was so focused this offseason, he turned down all external requests: 'I'm 95% football' Former MLB owner claims'despicable' San Francisco Giants are the reason the A's left Oakland Longtime NASCAR crew chief tells wild story about one of the sport's biggest characters WNBA finally embraces Caitlin Clark's stardom with unprecedented national TV schedule Why are the Mets so bad? Flyers mascot Gritty pens letter to fans ahead of first playoff game... eight years after he debuted NFL Draft prospect Rueben Bain Jr. mum about 2024 crash when publicly asked about it for first time Troy Aikman is selling'fire suites,' which are exactly what they sound like Fernando Mendoza's first pitch at Marlins game draws harsh reviews Steve Hilton praised for'offering solutions' in CA gubernatorial debate Middle East tensions escalate over US blockade, Iran's actions Michael Easter and Gary Brecka discuss the'choice' to live to be 100 Sen Ted Cruz calls new deadline with Iran'really consequential' RFK Jr confronted over'raccoon parts' on Capitol Hill Our democracy is not'in crisis,' Sen John Fetterman says The DOJ is'on the offense' here, Andrew Kolvet says OutKick ChatGPT predicted the first round of the NFL Draft and here's what it said Ultimate human vs. machine showdown as OutKick's Dan Z. takes on ChatGPT in a mock draft battle Where Is The Value In This NFL Draft? Jonathan Hutton & Chad Withrow ask Armando Salguero what position has the most value in this year's NFL draft I'm not sure why I do these things to myself, but I decided to go head-to-head with ChatGPT in a mock draft competition. I recently released my final mock draft, and then I asked ChatGPT to predict the entire first round. Below, you will see where we are the same and where we are different.

Taylor Sheridan's new war movie gets major update, legendary director attached LPGA star Nelly Korda sizzles on the beach, Dems won't stop dancing & Gia Duddy whips up a bikini lunch Paige Spiranac provides an update on'Great Cans' saga, fan's still MIA but others have picked up the slack Ivanka Trump has the angry libs on high alert as she slides into an amazing dress, Waffle House chaos & MEAT! Donald Trump makes odd'hair' comment to Danica Patrick at TPUSA event Islamabad enters'red zone' lockdown ahead of expected US-Iran peace talks Holocaust survivor known as'Crossing Guard Diva' goes viral for glam style House Ethics Committee weighs action against Rep. Cherfilus-McCormick'Sinister' links suspected in mysterious deaths of scientists Welcome to the numerous new Screencaps readers - trust me, you have to give this column two weeks to understand what's going on If you are one of the hundreds of thousands of new Screencaps readers who found this column on Monday, welcome back. You're about to become hooked. Just go ahead and clear your daily schedule at 9 a.m. for America's Best Daily Column, as named by the readers who've been with me for years. In some cases, readers have been with me for over a decade. This column is their talk radio.

Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive mixture models (SMMs), have been proposed as a potentially more expressive alternative. However, how to effectively use SMMs for VI and IS is still an open question as they do not provide latent variable semantics and therefore cannot use sampling schemes for classical MMs. In this work, we study how to circumvent this issue by designing several expectation estimators for IS and learning schemes for VI with SMMs, and we empirically evaluate them for distribution approximation. Finally, we discuss the additional challenges in estimation stability and learning efficiency that they carry and propose ways to overcome them. Code is available at: https://github.com/april-tools/delta-vi.

Davis, Drusvyatskiy, and Jiang showed that gradient descent with an adaptive stepsize converges locally at a nearly-linear rate for smooth functions that grow at least quartically away from their minimizers. The argument is intricate, relying on monitoring the performance of the algorithm relative to a certain manifold of slow growth -- called the ravine. In this work, we provide a direct Lyapunov-based argument that bypasses these difficulties when the objective is in addition convex and a has a unique minimizer. As a byproduct of the argument, we obtain a more adaptive variant than the original algorithm with encouraging numerical performance.

Accurately identifying patients with specific medical conditions is a key challenge when using clinical data from electronic health records. Our objective was to comprehensively assess when weakly-supervised prediction methods, which use silver-standard labels (proxy measures of the true outcome) rather than gold-standard true labels, perform well in rare-outcome settings like vaccine safety studies. We compared three methods (PheNorm, MAP, and sureLDA) that combine structured features and features derived from clinical text using natural language processing, through an extensive simulation study with data-generating mechanisms ranging from simple to complex, varying outcome rates, and varying degrees of informative silver labels. We also considered using predicted probabilities to design a chart review validation study. No single method dominated the other across all prediction performance metrics. Probability-guided sampling selected a cohort enriched for patients with more mentions of important concepts in chart notes. SureLDA, the most complex of the three algorithms we considered, often performed well in simulations. Performance depended greatly on selected tuning parameters. Care should be taken when using weakly-supervised prediction methods in rare-outcome settings, particularly if the probabilities will be used in downstream analysis, but these methods can work well when silver labels are strong predictors of true outcomes.

We initiate the study of language generation in the limit, a model recently introduced by Kleinberg and Mullainathan [KM24], under the constraint of differential privacy. We consider the continual release model, where a generator must eventually output a stream of valid strings while protecting the privacy of the entire input sequence. Our first main result is that for countable collections of languages, privacy comes at no qualitative cost: we provide an $\varepsilon$-differentially-private algorithm that generates in the limit from any countable collection. This stands in contrast to many learning settings where privacy renders learnability impossible. However, privacy does impose a quantitative cost: there are finite collections of size $k$ for which uniform private generation requires $Ω(k/\varepsilon)$ samples, whereas just one sample suffices non-privately. We then turn to the harder problem of language identification in the limit. Here, we show that privacy creates fundamental barriers. We prove that no $\varepsilon$-DP algorithm can identify a collection containing two languages with an infinite intersection and a finite set difference, a condition far stronger than the classical non-private characterization of identification. Next, we turn to the stochastic setting where the sample strings are sampled i.i.d. from a distribution (instead of being generated by an adversary). Here, we show that private identification is possible if and only if the collection is identifiable in the adversarial model. Together, our results establish new dimensions along which generation and identification differ and, for identification, a separation between adversarial and stochastic settings induced by privacy constraints.