Machine learning predictions are increasingly used to supplement incomplete or costly-to-measure outcomes in fields such as biomedical research, environmental science, and social science. However, treating predictions as ground truth introduces bias while ignoring them wastes valuable information. Prediction-Powered Inference (PPI) offers a principled framework that leverages predictions from large unlabeled datasets to improve statistical efficiency while maintaining valid inference through explicit bias correction using a smaller labeled subset. Despite its potential, the growing PPI variants and the subtle distinctions between them have made it challenging for practitioners to determine when and how to apply these methods responsibly. This paper demystifies PPI by synthesizing its theoretical foundations, methodological extensions, connections to existing statistics literature, and diagnostic tools into a unified practical workflow. Using the Mosaiks housing price data, we show that PPI variants produce tighter confidence intervals than complete-case analysis, but that double-dipping, i.e. reusing training data for inference, leads to anti-conservative confidence intervals and coverages. Under missing-not-at-random mechanisms, all methods, including classical inference using only labeled data, yield biased estimates. We provide a decision flowchart linking assumption violations to appropriate PPI variants, a summary table of selective methods, and practical diagnostic strategies for evaluating core assumptions. By framing PPI as a general recipe rather than a single estimator, this work bridges methodological innovation and applied practice, helping researchers responsibly integrate predictions into valid inference.

No Phone, No Social Safety Net: Welcome to the'Offline Club' Across Europe's largest cities, people are gathering for semi-silent, offline hangouts, in search of an experience that isn't mediated through their smartphones. On cue, the room fell silent. A man seated to my left at a long wooden table began to scratch at a piece of paper with a coloring pencil. To my right, another guy picked up a book. Across the way, someone buried themselves in a puzzle.

Apple could unveil Gemini-powered Siri in Feb. Amazon's latest round of layoffs will affect 16,000 workers The news was first leaked in an email mistakenly sent early to workers. Sydney, Australia - 2022-07-22 Amazon prime boxes and envelopes delivered to a front door of residential building. Amazon has confirmed that it's letting go of 16,000 workers and employees across its organization. In an announcement by company SVP Beth Galetti, she explained that Amazon was going through organizational changes to reduce layers and remove bureaucracy. Affected employees in the US will be given 90 days to look for another internal role and will receive severance pay if they do not find any.

Trump calls Ilhan Omar a'fraud' and suggests she staged shock syringe attack during Minneapolis town hall: 'She probably had herself sprayed' Nicola Peltz is'getting a $1MILLION a month allowance from her father Nelson' as Brooklyn Beckham's billionaire in-laws take him under their wing Iran braces for possible US attack as Trump's'beautiful armada' arrives in Middle East amid claims regime has slaughtered 30,000 protesters America's damning verdict on who's to blame for Minneapolis mayhem between Trump and far-left protesters Melania's shock role in Trump's showdown with Kristi Noem revealed: MARK HALPERIN's fly-on-wall account of Oval Office meeting... and who is ACTUALLY taking the fall for Alex Pretti shooting I've seen possessed children scream like beasts and strung up like puppets... these chilling exorcism cases PROVE hell is real Sickening proof Kanye West's apology was fake: MAUREEN CALLAHAN reveals heinous new Nazi slur everyone missed... and revolting REAL reason he wrote groveling letter Trader Joe's reveals its best products of 2026 in grocery's own Oscars - and there's a surprise winner School principal accused of shoplifting from Walmart using'stacking' method at self-checkout Harper Beckham, 14, puts on a stylish display in a fluffy coat and vintage Chanel bag in Paris with her family - after Nicola Peltz's heartbreaking comments about sister-in-law I was barely eating but kept gaining weight. Then I discovered the'taboo' cancer doctors NEVER talk about. Now sex will never be the same... don't ignore these signs Lost tomb of the mysterious'cloud people' unearthed after 1,400 years in'discovery of the decade' She's All That star Rachael Leigh Cook was a 2000s icon... see her now Revealed: The outdated British slang terms for sex that have been consigned to history - with'how's your father' topping the list Is your sex lingo up-to-date, or are your go-to terms giving away your age? The answer may lie in how many of these slang words and phrases you're still using. A new survey by Perspectus Global has revealed the once-popular terms that have been consigned to history.

Devastating impact of Minneapolis shooting on Trump is worse than expected: Poll reveals America's crushing verdict... and what he must do next Bodies are STILL in wreckage of private jet that crashed in Maine on Sunday, killing six including powerful lawyer's attorney wife School principal accused of shoplifting from Walmart using'stacking' method at self-checkout Melania's shock role in Trump's showdown with Kristi Noem revealed: MARK HALPERIN's fly-on-wall account of Oval Office meeting... and who is ACTUALLY taking the fall for Alex Pretti shooting I was barely eating but kept gaining weight. Then I discovered the'taboo' cancer doctors NEVER talk about. Now sex will never be the same... don't ignore these signs Harper Beckham, 14, puts on a stylish display in a fluffy coat and vintage Chanel bag in Paris with her family - after Nicola Peltz's heartbreaking comments about sister-in-law Devastating truth about Blind Side actor Quinton Aaron: More to this'than everyone is letting on', friends reveal... as co-star Sandra Bullock'monitors' situation The wild truth about my influencer sons, their psycho dad and how lawsuits nearly left them bankrupt - by Jake and Logan Paul's MOM Trump knifes'little Napoleon' Border Patrol commander over Minnesota mayhem as he declares: 'We'll de-escalate' Lost tomb of the mysterious'cloud people' unearthed after 1,400 years in'discovery of the decade' I've seen possessed children scream like beasts and strung up like puppets... these chilling exorcism cases PROVE hell is real There is a hidden battlefield within our world, where forces of light and darkness collide, believers say, in a conflict that sometimes spills into everyday life. In its most extreme form, the clash is described as possession: a person seemingly seized by demonic beings, their body overtaken, their voice and movements warped into something not quite human. For Anglican reverend Chris Lee, 43, this is not a theological abstraction but a reality he has lived with for nearly two decades.

The deployment of Artificial Intelligence in high-risk domains, such as finance and healthcare, necessitates models that are both fair and transparent. While regulatory frameworks, including the EU's AI Act, mandate bias mitigation, they are deliberately vague about the definition of bias. In line with existing research, we argue that true fairness requires addressing bias at the intersections of protected groups. We propose a unified framework that leverages Mixed-Integer Optimization (MIO) to train intersectionally fair and intrinsically interpretable classifiers. We prove the equivalence of two measures of intersectional fairness (MSD and SPSF) in detecting the most unfair subgroup and empirically demonstrate that our MIO-based algorithm improves performance in finding bias. We train high-performing, interpretable classifiers that bound intersectional bias below an acceptable threshold, offering a robust solution for regulated industries and beyond.

Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and strategic participation. This paper formulates prediction markets as Bayesian inverse problems in which the unknown event outcome \(Y\in\{0,1\}\) is inferred from an observed history of market-implied probabilities and traded volumes. We introduce a mechanism-agnostic observation model in log-odds space in which price increments conditional on volume arise from a latent mixture of trader types. The resulting likelihood class encompasses informed and uninformed trading, heavy-tailed microstructure noise, and adversarial or manipulative flow, while requiring only price and volume as observables. Within this framework we define posterior uncertainty quantification for \(Y\), provide identifiability and well-posedness criteria in terms of Kullback--Leibler separation between outcome-conditional increment laws, and derive posterior concentration statements and finite-sample error bounds under general regularity assumptions. We further study stability of posterior odds to perturbations of the observed price--volume path and define realized and expected information gain via the posterior-vs-prior KL divergence and mutual information. The inverse-problem formulation yields explicit diagnostics for regimes in which market histories are informative and stable versus regimes in which inference is ill-posed due to type-composition confounding or outcome--nuisance symmetries. Extensive experiments on synthetic data validate our theoretical predictions regarding posterior concentration rates and identifiability thresholds.

A border patrol agent scans the face of a driver in Minneapolis on 13 January 2026. A border patrol agent scans the face of a driver in Minneapolis on 13 January 2026. Immigration enforcement agents across the US are increasingly relying on a new smartphone app with facial recognition technology. The app is named Mobile Fortify. Simply pointing a phone's camera at their intended target and scanning the person's face allows Mobile Fortify to pull data on an individual from multiple federal and state databases, some of which federal courts have deemed too inaccurate for arrest warrants.

The government is consulting on a social media ban for under-16s, which would have a big impact on Meta's Instagram platform. The government is consulting on a social media ban for under-16s, which would have a big impact on Meta's Instagram platform. Campaigners decry ties with'Trump-supporting' tech firms after funding is accepted to develop state AI systems Ministers have accepted $1m (£728,000) from Meta, the US tech and social media company, to build AI systems for defence, national security and transport, sparking warnings about the UK government's "alarmingly close relationship with Trump-supporting US tech giants". The money from Mark Zuckerberg's company will be used to pay experts to "develop cutting-edge AI solutions to support national security and defence teams", the Department for Science, Innovation and Technology (DSIT) announced on Tuesday. The money will pay for four British AI experts, coordinated by the government-funded Alan Turing Institute, to "play a pivotal role in rewiring our healthcare, police, transport systems and more", said Ian Murray, the minister for data and digital government.

A technician works at an Amazon Web Services AI datacenter in New Carlisle, Indiana, on 2 October 2025. A technician works at an Amazon Web Services AI datacenter in New Carlisle, Indiana, on 2 October 2025. At Davos, tech CEOs laid out their vision for AI's world domination Tech chiefs waxed poetic about AI to delegates at Davos. Plus, the'human' drama of AI startups and why Tesla is thriving in Texas This week's edition is a team effort: my colleague Heather Stewart reports on the plans for AI's world domination at Davos; I examine how huge investments have followed AI companies with little to their names but drama and dreams; and Nick Robins-Early spotlights how lax regulation of autonomous driving in Texas allowed Tesla to thrive. When they weren't discussing Donald Trump, delegates at the World Economic Forum last week were being dazzled by the prospects for artificial intelligence.