Simpson's paradox poses a challenge in probabilistic inference and decisionmaking. Our study revisits the paradox by re-estimating its frequency with an unbiased data generation process and reaffirms that it is not an artifact of deficient data collection. Thus, it can lead to incorrect recommendations in fields as diverse as statistics, psychology, and artificial intelligence. We show that the paradox can be resolved by assuming a minimal -- though not necessarily observed -- common cause (or screening) variable for the involved random variables. In our approach, conditioning on this minimal common cause establishes the correct association between events, which coincides with the conditioning (i.e., fine-grained) option of the original Simpson paradox. This resolution applies to both discrete cases of binary variables and continuous settings modeled by Gaussian variables. For a non-minimal common cause, the resolution of the paradox is possible, but detailed knowledge of the common cause is required. Our findings extend traditional understandings of the paradox and offer practical guidance for resolving apparent contradictions in probabilistic inference, ultimately enhancing decision-making processes. This point is illustrated by several examples.

Simpson's paradox poses a challenge in probabilistic inference and decision-making. Our study revisits the paradox by re-estimating its frequency with an unbiased data generation process and reaffirms that it is not an artifact of deficient data collection. Thus, it can lead to incorrect recommendations in fields as diverse as statistics, psychology, and artificial intelligence. We show that the paradox can be resolved by assuming a minimal -- though not necessarily observed -- common cause (or screening) variable for the involved random variables. In our approach, conditioning on this minimal common cause establishes the correct association between events, which coincides with the conditioning (i.e., fine-grained) option of the original Simpson paradox. This resolution applies to both discrete cases of binary variables and continuous settings modeled by Gaussian variables. For a non-minimal common cause, the resolution of the paradox is possible, but detailed knowledge of the common cause is required. Our findings extend traditional understandings of the paradox and offer practical guidance for resolving apparent contradictions in probabilistic inference, ultimately enhancing decision-making processes. This point is illustrated by several examples.

No one can say for sure what's going on in the president's head. His 25 greatest obsessions can get us a little closer. This is the year the first baby boomers--those born in 1946--turn 80, and that cohort includes Donald Trump. We have all recently lived through what it means to have an 80-year-old commander in chief, but at a political moment that's simultaneously more horrific, erratic, and just plain befuddling than anything this country has seen in ages, we wanted to understand the brain of 80-year-old president. Plenty of people are trying to discern whether his recent rants and raves are due to a more serious cognitive decline--we understand the instinct; we've done it too --but we went a different (if related) route. The more we dug into Trump's many fixations, the more we realized that this man still thinks he lives in the 1980s. We also discovered--without too much surprise--that he often seems to fundamentally misunderstand the works he treasures most deeply. These items might not replace a brain map, but they do create a certain holistic view of what animates and splinters Trump's mind. Sometimes, they just help explain his worldview. Other times, they seem to have had real influence on policy and the America that Trump is trying to create. Welcome to Trump Brain, the 25 things that define who the president is--and what he wants. Please enable javascript to fully experience this interactive. When millions of people took to the streets in October to protest Trump's authoritarianism, the president responded by dunking on his critics online. Specifically, he posted an A.I.-generated video of a fighter jet, piloted by himself in a literal crown, dropping human excrement onto the crowds. It was perhaps Trump's most juvenile use of A.I. slop yet--the kind of low-quality, feverish content made possible by artificial intelligence. Trump undoubtedly is the perfect president for the A.I. slop era. In some ways, this is because he's the ideal audience for it: Like many older internet users delighted by the technology, Trump seems to enjoy mindless, cartoonish, childish content. One of the videos he shared depicted him playing soccer with Cristiano Ronaldo in the Oval Office.

Take the Portland Trail Blazers +2.5 in Game 3 Shocker! Kyle Brandt-Seth Rollins on-set spat was staged Tigers look to exploit Reds' struggles at home as Framber Valdez takes the mound in Cincinnati Watch as Eagles steal Makai Lemon with wild phone call: 'Why is Philly calling me?' Giants' draft pick has intense Jaxson Dart message: 'I'm ready to die for you' Donald Trump uses Pete Rose to justify soldier's alleged shady Maduro bet, and he's not wrong Ex-Michigan football coach Sherrone Moore's mistress reveals he got her pregnant during relationship Giants' bizarre draft decisions leave star player frustrated as true needs go unfulfilled in first round Rueben Bain's short arms and tragic car accident history contributed to his NFL Draft slide Sherrone Moore accuser Paige Shiver speaks out in new interview: he'had complete control over me' Megan Rapinoe calls on traditional WNBA media to be replaced with those who'understand queer culture' The NFL Draft continues to be one of the worst'sporting events' of the year'Fox & Friends' hosts learn country line dancing in Houston Veterans cheer Trump's order on psychedelic drugs to treat PTSD'Fox & Friends' hosts'get their Texas on' with Tecovas boots'Fox & Friends' kicks off the Fox News America 250 Tour in Houston Country artist Rich O'Toole joins'Fox & Friends' in Houston IDF finds'ambulance used by Hezbollah to conceal weapons' Hegseth shuts down reporter's EXTREME question OutKick 49ers GM John Lynch skeptical of Rams' decision to draft QB Ty Simpson with No. 13 overall pick Lynch called Simpson'a good football player' but noted the pick'surprised everybody' The San Francisco 49ers traded out of the NFL Draft's first round on Thursday, so general manager John Lynch didn't have a player to discuss when he met with reporters. No problem, because he started talking players a couple of division rivals drafted. Lynch commented on what the Arizona Cardinals and Los Angeles Rams did. San Francisco 49ers general manager John Lynch speaks at the NFL Scouting Combine at the Indiana Convention Center on Feb. 24, 2026.

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.

A nd so Fortnite has done it again. Over the past five years, developer Epic Games maintained the relevance and awareness of its ageing online shooter by churning out pop culture collaborations, from Marvel to John Wick to Sabrina Carpenter. For limited periods, players get to take part in the game as their favourite movie characters and music artists, an arrangement that provides refreshed audience numbers for the game - and a tidy revenue stream for the brands. This month, the Fortnite island has become a miniature Springfield, complete with popular characters and well-known locations. If you want to play as Homer and shoot up Moe's Tavern, you can.

Last week, an American-Israeli company that claims it's developed proprietary technology to cool the planet announced it had raised $60 million, by far the largest known venture capital round to date for a solar geoengineering startup. The company, Stardust, says the funding will enable it to develop a system that could be deployed by the start of the next decade, according to Heatmap, which broke the story. As scientists who have worked on the science of solar geoengineering for decades, we have grown increasingly concerned about emerging efforts to start and fund private companies to deploy technologies that could alter the climate of the planet. We also strongly dispute some of the technical claims that certain companies have made about their offerings. This story is part of Heat Exchange, MIT Technology Review's guest opinion series offering expert commentary on legal, political and regulatory issues related to climate change and clean energy. Can "The Simpsons" really predict the future?

Distinguishing correlation from causation is a fundamental challenge in machine intelligence, often representing a critical barrier to building robust and trustworthy systems. While Pearl's $\mathcal{DO}$-calculus provides a rigorous framework for causal inference, a parallel challenge lies in its physical implementation. Here, we apply and experimentally validate a quantum algorithmic framework for performing causal interventions. Our approach maps causal networks onto quantum circuits where probabilistic links are encoded by controlled-rotation gates, and interventions are realized by a structural remodeling of the circuit -- a physical analogue to Pearl's ``graph surgery''. We demonstrate the method's efficacy by resolving Simpson's Paradox in a 3-qubit model, and show its scalability by quantifying confounding bias in a 10-qubit healthcare simulation. Critically, we provide a proof-of-principle experimental validation on an IonQ Aria quantum computer, successfully reproducing the paradox and its resolution in the presence of real-world noise. This work establishes a practical pathway for quantum causal inference, offering a new computational tool to address deep-rooted challenges in algorithmic fairness and explainable AI (XAI).

AI Expert Marva Bailer explains to Fox News Digital Hank Azaria's opinion piece about humanity and AI matters. "The Simpsons" star Hank Azaria has voiced his fears over artificial intelligence in a new opinion piece. The actor, who has been with the show since 1989, wrote an opinion essay for The New York Times, worrying AI "will be able to recreate the sounds of the more than 100 voices I created for characters on'The Simpsons.'" He continued, "It makes me sad to think about it. Not to mention, it seems just plain wrong to steal my likeness or sound -- or anyone else's."

Federated learning (FL) is a promising technology for data privacy and distributed optimization, but it suffers from data imbalance and heterogeneity among clients. Existing FL methods try to solve the problems by aligning client with server model or by correcting client model with control variables. These methods excel on IID and general Non-IID data but perform mediocrely in Simpson's Paradox scenarios. Simpson's Paradox refers to the phenomenon that the trend observed on the global dataset disappears or reverses on a subset, which may lead to the fact that global model obtained through aggregation in FL does not accurately reflect the distribution of global data. Thus, we propose FedCFA, a novel FL framework employing counterfactual learning to generate counterfactual samples by replacing local data critical factors with global average data, aligning local data distributions with the global and mitigating Simpson's Paradox effects. In addition, to improve the quality of counterfactual samples, we introduce factor decorrelation (FDC) loss to reduce the correlation among features and thus improve the independence of extracted factors. We conduct extensive experiments on six datasets and verify that our method outperforms other FL methods in terms of efficiency and global model accuracy under limited communication rounds.