Background on Principal Component Analysis Principal component analysis (PCA) is a method widely used by practitioners for learning features of high-dimensional data [15]. It is a dimension reduction technique that represents the data in lower dimensions, often with the aim of exploratory analysis or visualization. PCA can also be used as a data preprocessing step, for instance in regression analysis. While PCA is familiar and commonplace for understanding behavior in the data's'bulk', only recently have similar methods been proposed for understanding high-dimensional extremes. The aim of this chapter is to review and compare recent approaches for extremal PCA. 1

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.

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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.

Plus: Anthropic has called for a global slowdown in AI development. The Meta hack shows there's more to AI security than Mythos On Monday, reports emerged that attackers had used Meta's AI customer support agent to steal Instagram accounts. Their approach was simple: they asked the agent to link the accounts to email addresses they controlled, and it complied. Since Anthropic announced that its Mythos model was too good at hacking for a general release, cybersecurity concerns have focused on the risk of superpowered AI systems overwhelming computer infrastructure. But the Instagram hack shows that far simpler exploits can still cause damage. As companies offload more work to AI, these comparatively unsophisticated attacks are becoming harder to ignore.

A seemingly simple set of rules kicks off a kind of mathematical magic trick, which has kept great minds busy since the 1930s. Almost a century ago, a mathematician came up with a puzzle that was so seemingly simple and yet so fiendishly difficult that it has been distracting other mathematicians ever since. It has become a meme that jumps from brain to brain, with many people claiming to have solved it, only to have their hopes dashed as the proof unravels. And be warned - once I explain the rules, you will immediately want to start playing around with it yourself, and I take no responsibility for how much of your time you waste. It starts a bit like a magic trick.

On June 5, reported that attackers had been using Meta's AI customer support agent to steal Instagram accounts. Their approach was simple: They asked the agent to link the accounts to email addresses that they controlled, and the agent complied. One attacker broke into the dormant Obama White House account and made pro-Iran posts; others took over accounts with valuable, single-word handles, possibly in order to sell them. AI cybersecurity concerns are nothing new. Since Anthropic announced in April that its Mythos model was too good at hacking to be released to the general public, commentators, researchers, and federal officials alike have fixated on the idea that superpowered AI systems could lay waste to our computer infrastructure. That's not quite what this Instagram hack was: There, AI was the target rather than the attacker, and the method was far simpler than anything Mythos would cook up. But as companies offload more work to AI, these comparatively unsophisticated attacks could wreak their own havoc. "As AI becomes more and more widely used--especially when AI is more and more widely used to automate our work flows, like account recovery--I think attackers are going to be more and more motivated to attack AI itself," says Neil Gong, a professor of electrical and computer engineering at Duke University.