In this work, we revisit the problem of active sequential prediction-powered mean estimation, where at each round one must decide the query probability of the ground-truth label upon observing the covariates of a sample. Furthermore, if the label is not queried, the prediction from a machine learning model is used instead. Prior work proposed an elegant scheme that determines the query probability by combining an uncertainty-based suggestion with a constant probability that encodes a soft constraint on the query probability. We explored different values of the mixing parameter and observed an intriguing empirical pattern: the smallest confidence width tends to occur when the weight on the constant probability is close to one, thereby reducing the influence of the uncertainty-based component. Motivated by this observation, we develop a non-asymptotic analysis of the estimator and establish a data-dependent bound on its confidence interval. Our analysis further suggests that when a no-regret learning approach is used to determine the query probability and control this bound, the query probability converges to the constraint of the max value of the query probability when it is chosen obliviously to the current covariates. We also conduct simulations that corroborate these theoretical findings.

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.

Outside of Japan, Google's chatbot is accessible on both desktop and iOS. Google has added a new sidebar to Chrome that allows users to access Gemini from any of their tabs. After debuting in the US, Gemini in Chrome is making its way to more markets. Starting today, Google is rolling out Chrome's built-in chatbot to users in Asia and the Pacific, including Australia, Indonesia, Japan, the Philippines, Singapore, South Korea and Vietnam. The expansion comes after Google earlier this year made Gemini in Chrome available to people in Canada, India and New Zealand .

Nancy Guthrie sheriff's appalling past revealed: Beat handcuffed suspect so badly he needed intensive care, used VILE language about woman and lied in sworn statement Vance grounded at White House as Iran peace talks in turmoil and Trump declares: 'I expect to be bombing' New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Ark of the Covenant's final resting place pinpointed by archaeologists as fresh search begins Ritzy Bay Area town torn apart after teacher's daughter, 16, crashed car while speeding and killed four friends... then posted a TikTok video that poured fuel on the flames Jordon Hudson extends her control over Bill Belichick's empire with secret move that is set to leave his family and friends furious Two CIA officers killed in Mexico when their car skidded off ravine and exploded after meeting about bust of'largest ever drug lab' Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' AMANDA PLATELL: Why Sarah Ferguson - with the ghost of Princess Diana at her side - is ready to sensationally blow up the Royal Family. She knows ALL their secrets... Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran Team USA Olympics star Noah Lyles slammed for'horrible' reaction to his wife's wedding dress reveal In honour of the Queen's (purple!) reign: Kate mirrors late monarch's colourful wardrobe and wears her pearl earrings and necklace How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. The new'posh' drug that's easier to order than Uber Eats - and why all my middle-class friends have ditched booze and cocaine for it: JANA HOCKING Fury as murderer marries pen pal behind bars... as teenage victim's mom says: 'I'm serving a life sentence without my son' Autistic woman, 24, worked hard to build independent life for herself... now she's PARALYZED thanks to selfishness of stranger Chilling warning from Nobel physicist as date is set for humanity's final destruction The winner of the Nobel Prize in Physics has issued a stark warning to humanity, saying it could face an existential catastrophe within roughly 35 years. David Gross, who shared the 2004 Nobel Prize in Physics, warned that'due to the danger of nuclear war,' humankind may have just a little more than three decades left.

Elon Musk was summoned by the French authorities for a voluntary interview that had been planned to take place on Monday. Elon Musk was summoned by the French authorities for a voluntary interview that had been planned to take place on Monday. Elon Musk did not appear on Monday for a voluntary interview with lawyers in Paris, who had summoned the American tech billionaire over an investigation into his social media platform X and AI chatbot Grok. The prosecutors told AFP that they had "taken note of the absence of the first people summoned", without mentioning Musk's name. The billionaire called the French authorities involved "retards" weeks earlier in a French-language post on X .

Inside the bird eat bird world of'beak jousting.' More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. Even without an upper beak, one bird in New Zealand is defying odds at the top of the pecking order. Bruce is a rescued kea () parrot that is the alpha male among his species living at the Willowbank Wildlife Reserve in Christchurch, New Zealand.

Ritzy Bay Area town torn apart after teacher's daughter, 16, was behind wheel when four friends died in high-speed crash... then she posted a TikTok video that poured fuel on the flames Two CIA officers killed in Mexico when their car skidded off ravine and exploded after meeting about bust of'largest ever drug lab' Nancy Guthrie sheriff's appalling past revealed: Beat handcuffed suspect so badly he needed intensive care, used VILE language about woman and lied in sworn statement Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Ark of the Covenant's final resting place pinpointed by archaeologists as fresh search begins Fury as murderer marries pen pal behind bars... as teenage victim's mom says: 'I'm serving a life sentence without my son' Insiders claim failed AI rollout could be to blame for Tim Cook's departure from Apple - as one says'the AI era requires a different kind of leadership' Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' AMANDA PLATELL: Why Sarah Ferguson - with the ghost of Princess Diana at her side - is ready to sensationally blow up the Royal Family. She knows ALL their secrets... Team USA Olympics star Noah Lyles slammed for'horrible' reaction to his wife's wedding dress reveal In honour of the Queen's (purple!) reign: Kate mirrors late monarch's colourful wardrobe and wears her pearl earrings and necklace US troops board second tanker as Iran is accused of breaking ceasefire'numerous times' How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. The new'posh' drug that's easier to order than Uber Eats - and why all my middle-class friends have ditched booze and cocaine for it: JANA HOCKING Autistic woman, 24, worked hard to build independent life for herself... now she's PARALYZED thanks to selfishness of stranger READ MORE: McDonald's is testing humanoid ROBOTS in Shanghai During last year's shambolic Beijing robot half marathon, humanoid machines tripped, shuffled, and occasionally shattered into pieces as they collapsed under the strain. But 12 months later, supporters looked on in awe as a new generation of speedy robotic racers left the human athletes in the dust.

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. While beautiful, Bradford pear trees also stink. Breakthroughs, discoveries, and DIY tips sent six days a week. The sun is out, the streets are humming, the days are getting longer, and the air smells like like um say, can anyone else smell that? All over America, spring is getting smellier every year, and the culprit is the Bradford pear, a tree that gained popularity in the mid-20 century for its ornamental properties.

It took 120 years to figure out the forgotten fossil belonged to an extinct giant echidna. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. An illustration of what Owen's giant echidna may have looked like. The now extinct megafauna was up to three feet-long. Breakthroughs, discoveries, and DIY tips sent six days a week.

Sam Altman speaks during the BlackRock infrastructure summit on 11 March in Washington DC. Sam Altman speaks during the BlackRock infrastructure summit on 11 March in Washington DC. How a fiery attack on Sam Altman's home unfolded Molotov cocktail attack on OpenAI CEO's home comes amid growing discontent against artificial intelligence I n the early hours of 10 April, a man approached the gate of OpenAI CEO Sam Altman's house in San Francisco and hurled a molotov cocktail at the building before fleeing. Federal and California state authorities have charged Moreno-Gama with a range of crimes including attempted arson and attempted murder. His parents issued a statement this week saying that their son had recently suffered a mental health crisis.