South Korean President Lee Jae Myung is placing his hopes on former Naver Chief Executive Han Seong Sook to help better use the nation's tech expertise for future growth and ensure its benefits spread more widely through the economy. Han will become the country's second female premier, assuming her appointment is approved by the national assembly, elevating a former technology executive to one of the nation's highest political posts. The tapping of Han underscores Lee's commitment to shoring up future growth of the domestic economy and the need to leverage a wider range of industries. During her five years at the helm of Naver, a company sometimes called the Google of Korea, Han helped broaden its revenue streams beyond its search engine model to also draw on e-commerce, fintech and content generation. In a time of both misinformation and too much information, quality journalism is more crucial than ever. By subscribing, you can help us get the story right.

Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional. We propose DeSI (Deep Single-Index Fréchet Regression), a semiparametric framework for regression with metric space-valued outputs and multivariate inputs that assumes a single-index structure for the conditional Fréchet mean. DeSI estimates an interpretable index direction, which quantifies the relative importance of inputs, using a deep neural network, and performs Fréchet regression along the resulting one-dimensional index in the target metric space. This structure mitigates the curse of dimensionality while retaining interpretability, which stands in contrast to standard deep neural networks. We establish theoretical guarantees for DeSI, including uniform approximation and convergence rates, and demonstrate its strong predictive performance through simulations on distributions, networks, and symmetric positive-definite matrices, as well as an application to compositional mood data from New Jersey.

We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two agents each observe different coordinates of $m$ i.i.d. sub-Gaussian samples and communicate a limited number of bits to a central server. While Rahmani et al. [2025] established nearly tight bounds for dense (unstructured) cross-covariance matrices, we investigate whether imposing elementwise $s$-sparsity on the cross-covariance $C_{21}$ can reduce the required communication and sample complexity. In contrast to the horizontal-split setting, where Braverman et al. [2016] showed that sparsity does not reduce communication cost for mean estimation, we prove that sparsity does help for cross-covariance estimation in the vertical split. Specifically, we establish minimax lower bounds showing that the communication budget per agent scales as $B_k = Ω(σ^4 d_k\, s' \log(d_1 d_2/s')/\varepsilon^2)$ and the sample complexity for cross-covariance estimation as $m = Ω(σ^4\, s' \log(d_1 d_2/s')/\varepsilon^2)$, where $s' = s \wedge d_{\min}$. For the $1$-sparse case, this yields an exponential improvement from $d_1 d_2$ to $\log(d_1 d_2)$ compared to the dense rate. Our lower bounds are established via Fano's method with an explicit sparse packing using a Varshamov--Gilbert-type argument for signed partial permutation matrices combined with the Conditional Strong Data Processing Inequality of Rahmani et al. [2025]. We show the bounds are tight with a matching achievable scheme, based on covering-net quantization and entry-wise hard thresholding, that attains the $s$-sparse lower bound up to polylogarithmic factors.

Decision-making in complex systems often requires understanding counterfactuals of general, potentially highdimensional, interventions with limited data. Collecting sufficient data for every counterfactual in complex systems may be near impossible due to cost or ethical reasons. With the recent growth in expressivity and power in generative modeling, generative models that can synthesize counterfactual outcomes under generalized interventions stand as a viable solution for supporting robust decision-making in real-world systems. In an ideal world, we may simply train a generative model with the data we have, and sample from the generator under the intervention of interest. Counterfactual generative modeling may fail with such an approach due to confounding bias. Correlations observed in the sampled data may be mistaken for true causal effects, yielding incorrect downstream decisions. For example, generating medical images under changes in intervention dose can help track disease progression and identify optimal dosing strategies. However, if the training data primarily consisted of those who were responsive to intervention (e.g., younger populations), then the generator would identify the ranges in the data as effective even if this does not hold for different populations (e.g.

Identifying most influential sets (MIS) - size-$k$ subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over $\binom{n}{k}$ subsets. For estimands with linear-fractional leave-set-out effects, we show that MIS selection reduces to a one-parameter sequence of top-$k$ problems. Dinkelbach's method yields an algorithm with $\mathcal{O}(n)$ cost per iteration and finite termination. For fixed residualized inputs, the algorithm returns a globally optimal set for the univariate ratio objective, including the oracle-residualized partial linear model. With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective; exact set recovery follows under a separation condition. Simulations and applications show that the method recovers exact MIS that were previously computationally inaccessible.

Caitlyn Jenner biographer and Robin Riker's ex William Hasley found dead on hiking trail at 78 Disgraceful texts'hot' teacher sent boy, 17, who she had illegal sex with where she moaned about her HUSBAND Everyone always said I cleared my throat a lot. But then I developed shoulder pain and doctors discovered the sinister cause... the world's deadliest cancer. Don't leave it too late like I did Urgent recall for 1.1m vehicles over fears they could spontaneously CATCH FIRE even when parked Moment Real Housewives star Lenny Hochstein's sexual assault accuser'dances' as she leaves Star Island mansion - before filing $100k civil lawsuit Leaked transcript of UNAIRED 60 Minutes interview exposes REAL reason'callous' CBS star Scott Pelley'deserved to be fired' Disturbing new death scene photos show tech whistleblower's haunting final moments... as forensic report casts doubt on suicide claims: 'Execution angle' 'Great' mom, 32, tried to gas herself and her three young kids to death after inviting them to'popcorn sleepover' in car, prosecutors allege The porn-fuelled fantasy middle-class husbands are desperate to try with their wives... and it almost always ends in divorce: JANA HOCKING The historic steel mill that helped build America was written off for dead. Medical student, 24, died by suicide in his white coat a day after he was suspended for alleged'inappropriate' behavior towards female patient, lawsuit alleges, as his heartbreaking goodbye note to parents is revealed John Oliver's private panic: Late-night curse spreads and host prepares for worst as insiders reveal his desperate'plan B'... and the industry whispers swirling about his fate Woke Vegas school compared boy to racist cross burner over pro-ICE stickers and expelled him... but did not punish pro-migrant students for class walkout, lawsuit alleges Gaming influencer Alex Cimo dies'very suddenly' aged 32 just a month after'refusing to accept his fate' Mother's final words before she was shot dead'by new husband' in front of her two young children All the backstage gossip from Miami Swim Week: Insider exposes'catty' VIP's diva demands... STEALING... and'morbidly embarrassing' celeb moment everyone is whispering about READ MORE: Gen Z are'zebra striping' on nights out to avoid hangovers From drinking'Tiger's milk' to soaking socks in vodka, many booze-loving Brits will try just about anything to avoid a hangover. Now, a new anti-hangover method is emerging on social media - avoiding rounds at the pub.

Proponents and critics of artificial intelligence often compare the technology to industrial automation--really, it's more like an intern. One summer during high school, I took a temporary job writing computer programs for a consulting firm. Each morning, I drove through rush-hour traffic to an office park near Princeton, New Jersey, on the crowded Route 1 corridor. At a desk in some sort of equipment room, I coded quick-and-dirty database tools for internal use. One of my programs simplified the process of logging hours into timesheets.

He is about to take SpaceX public--pushing other AI companies to do the same. Elon Musk is about to set in motion a chain of events that will reshape the global financial order. For starters, when SpaceX formally goes public next week, he is all but guaranteed to become the world's first trillionaire. His rocket company is targeting a valuation of $1.77 trillion, which would make it one of the 10 biggest companies in the world--bigger than Meta, Walmart, and, for that matter, Tesla. All of this activity is less about colonizing Mars and more about providing the infrastructure for the AI boom: Musk wants to use his rockets to launch data centers into space, where there is abundant solar power to harvest.

Flood of AI'garbage' is pushing open-source developers to the limit A viral cartoon about open-source software shows a teetering pile of boxes labelled "all modern digital infrastructure" and one tiny box right at the bottom, propping up the whole lot: "a project some random person in Nebraska has been thanklessly maintaining since 2003". That's the reality of open source: every website, application and operating system relies on it. Modern society couldn't function without it, and yet it's written by volunteers in their spare time. But the growing burden caused by a flood of AI-generated code is causing many to burn out and leave the community altogether, threatening the future of open-source software. 'Flashes of brilliance and frustration': I let an AI agent run my day AI models are making it easier and easier to generate code to build new features, fix bugs or create entire new projects at the click of a button.

A painting bought for less than $100 (£75) in a US charity shop in the 1960s has sold for almost £190,000 at auction. Art teacher Helene Plotkin bought the work by Scottish Colourist FCB Cadell in White Plains, New York in 1966, unaware of its true value. The painting, Interior: The Lady in Black, hung in her living room for 60 years - but the artist's signature was illegible and was only recently identified. It sold for £189,200, including buyer's premium, in Edinburgh as part of Lyon & Turnbull's Scottish painting and sculpture auction. The background to the painting only became clear when Helene's son Barry began his own research into it and took it for a valuation last year.