Furthermore, weprovethat, under mild assumptions, a slight variation of WQL enjoys desirable theoretical properties in the tabular setting.

The astonishing moment Scott Bessent returns to interview noticeably shaken after'Situation Room' call from Trump Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back'Awakening' of terrorist sleeper cells sparks World Cup PANIC: Undercover officer reveals'once in 25 year' threat... and America's'Achilles heel' Trump's Iran war death toll climbs to 13 after all crew onboard US refueling plane died in crash Mother reveals awful sight that greeted her when she opened Walmart in-store oven to find daughter, 19, baked to death inside... and denies suggestions it was suicide Recall of cream cheeses upgraded to most serious risk over contamination with deadly bacteria... 'reasonable probability of death' San Francisco's most iconic mansion is bought by ALGERIAN government for $10m Iran-linked cyberattack on US is'first drop of blood' as experts reveal alarming new threat to homeland I've spent 25 years treating patients with autism. This is the truth about the condition that many people don't want to hear: DR MAX PEMBERTON Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Airfares have already doubled on key routes and are getting worse - here's when to book to avoid the worst prices I was pregnant when I discovered my husband was cheating with my male doctor. I still let him deliver our baby... our arrangement may shock you Maker of Mounjaro writes scathing letter to warn of dangerous'chemical reactions' in knock-off versions of weight-loss drug Cher's son Chaz Bono weds'love of my life' Shara Blue Mathes in front of famous mom in Hollywood A powerful'megastorm' set to slam a large swatch of the US could ultimately rank among the most impactful weather events of the year so far. The sprawling system is forecast to sweep from the central Plains into the Midwest and East between Sunday and Monday, bringing widespread travel disruptions and power outages . Blizzard conditions could hit parts of Wisconsin, Michigan, Iowa, northern Illinois and southeastern Minnesota, where forecasters warned that heavy snow and fierce winds may create dangerous whiteout conditions.

Yellowstone's ravens may memorize wolf hunting hotspots--to feast The birds will fly over 90 miles to dine where wolves have drawn blood. Breakthroughs, discoveries, and DIY tips sent six days a week. When wolves are on the hunt, a kill rarely goes unnoticed for long. In the elk-and deer-rich areas of northern Yellowstone National Park, ravens are often among the first scavengers to arrive on the scene, swooping down to feast on scraps left behind by the howling canines. Field biologists have long assumed that the birds simply follow wolves as they track and take down their prey.

Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Millions across 10 US states brace for'severe' tornado outbreak in just hours Millions of Americans have been told to prepare for a possible tornado outbreak on Tuesday. Meteorologists warned that severe thunderstorms are expected from the southern Plains into the southern Great Lakes vicinity starting between 4pm and 6pm CT. The states currently at risk include Illinois, Indiana, Missouri, Iowa, Texas, Oklahoma, Michigan, Ohio, Wisconsin and Tennessee .

ROTC students at Old Dominion subdued and killed ISIS-linked gunman who left one dead, two wounded after shouting'Allahu Akbar' and opened fire Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Meteorologists have issued a warning to millions of Americans as a dangerous storm system is set to sweep across a large swath of the country on Friday. Parts of Texas, Oklahoma, Kansas, Missouri, Arkansas, Iowa, Illinois and Wisconsin could see hurricane-force wind gusts of up to 80 mph, tornadoes and hail as the powerful system intensifies. The threat comes after severe storms already unleashed damaging winds, large hail and tornadoes from Texas to Kansas through Thursday night, according to AccuWeather.

Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Alexander brothers' alleged HIGH SCHOOL gang rape video: Classmates speak out on sick'taking turns' footage... as creepy unseen photos are exposed Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Live Nation executives mocked'stupid' concert-goers in emails where they bragged about how to best rip them off: '$60 for closer grass' NFL superstar Xavier Worthy spills all on Travis Kelce, the Chiefs' struggles... and having Taylor Swift as his No 1 fan Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Nancy Mace throws herself into Iran warzone as she goes rogue on Middle East rescue mission: 'I AM that person' Hidden toxins in kids' treats EXPOSED: Health guru Jillian Michaels' sit-down with Casey DeSantis reveals dangers lurking in popular foods Interactive map reveals your nearest nuclear shelter and states that are MOST exposed... amid fears of US attack: Make an emergency plan now The fear of a nuclear apocalypse has reached levels not seen in decades as the US and Israel launch a deadly new conflict with Iran, raising alarms across capitals and prompting emergency diplomatic efforts to prevent a wider war. For Americans, the pressing question may soon shift from geopolitics to personal preparedness, including where the nearest fallout shelter is located and how to protect themselves if tensions escalate further. There is currently no public list of active shelters available for everyday Americans, since most are defunct or privately owned. But survival expert and Air Force veteran Sean Gold has built his own fallout shelter map, revealing that the vast majority of these radiation bunkers are scattered throughout America's largest cities. The map can be found on his survival guide website, TruePrepper .

Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' The US and Israel have launched one of their most aggressive military operations in decades, dramatically escalating tensions with Iran and raising fears of a wider regional war. As the risk of retaliation grows, a sobering new projection is forcing Americans to confront a chilling question: What would happen if the conflict spiraled into a nuclear strike on US soil? To help visualize that threat, a newly circulated map models the potential devastation, showing how a large-scale nuclear attack could impact major population centers across the country.

ROTC students at Old Dominion subdued and killed ISIS-linked gunman who left one dead, two wounded after shouting'Allahu Akbar' and opened fire Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' READ MORE: 38,000 gallons of bottled water recalled because of'foreign substance' More than 650,000 plastic water bottles have been recalled after they were produced'under insanitary conditions.' The FDA issued an alert for Valley Springs 100% Natural Bottled Water, noting the recall was voluntarily initiated by the Wisconsin-based Valley Springs Artesian Gold. While details are limited, insanitary conditions mean products were prepared, packed, or held under conditions that could allow them to become contaminated with filth or rendered injurious to health.

This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where depth is constrained to be less than the number of classes -- a limitation that proves too rigid for complex classification problems. Our extensions improve performance in multi-class settings with unequal variance-covariance structures and nonlinear class separations by allowing more splits and more flexible class groupings in the projection pursuit computation. Proposing algorithmic improvements is straightforward; demonstrating their actual utility is not. We therefore develop two visual diagnostic approaches to verify that the enhancements perform as intended. Using high-dimensional visualization techniques, we examine model fits on benchmark datasets to assess whether the algorithm behaves as theorized. An interactive web application enables users to explore the behavior of both the original and enhanced classifiers under controlled scenarios. The enhancements are implemented in the R package PPtreeExt.

Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these limitations, but have problems of their own. The key step of specifying prior distributions in BNNs is no trivial task, yet is often skipped out of convenience. In this work, we propose a new class of prior distributions for BNNs, the Dirichlet scale mixture (DSM) prior, that addresses current limitations in Bayesian neural networks through structured, sparsity-inducing shrinkage. Theoretically, we derive general dependence structures and shrinkage results for DSM priors and show how they manifest under the geometry induced by neural networks. In experiments on simulated and real world data we find that the DSM priors encourages sparse networks through implicit feature selection, show robustness under adversarial attacks and deliver competitive predictive performance with substantially fewer effective parameters. In particular, their advantages appear most pronounced in correlated, moderately small data regimes, and are more amenable to weight pruning. Moreover, by adopting heavy-tailed shrinkage mechanisms, our approach aligns with recent findings that such priors can mitigate the cold posterior effect, offering a principled alternative to the commonly used Gaussian priors.