We address the problem of quickest change detection in Markov processes with unknown transition kernels. The key idea is to learn the conditional score $\nabla_{\mathbf{y}} \log p(\mathbf{y}|\mathbf{x})$ directly from sample pairs $( \mathbf{x},\mathbf{y})$, where both $\mathbf{x}$ and $\mathbf{y}$ are high-dimensional data generated by the same transition kernel. In this way, we avoid explicit likelihood evaluation and provide a practical way to learn the transition dynamics. Based on this estimation, we develop a score-based CUSUM procedure that uses conditional Hyvarinen score differences to detect changes in the kernel. To ensure bounded increments, we propose a truncated version of the statistic. With Hoeffding's inequality for uniformly ergodic Markov processes, we prove exponential lower bounds on the mean time to false alarm. We also prove asymptotic upper bounds on detection delay. These results give both theoretical guarantees and practical feasibility for score-based detection in high-dimensional Markov models.

Causal structure learning has long been the central task of inferring causal insights from data. Despite the abundance of real-world processes exhibiting higher-order mechanisms, however, an explicit treatment of interactions in causal discovery has received little attention. In this work, we focus on extending the causal additive model (CAM) to additive models with higher-order interactions. This second level of modularity we introduce to the structure learning problem is most easily represented by a directed acyclic hypergraph which extends the DAG. We introduce the necessary definitions and theoretical tools to handle the novel structure we introduce and then provide identifiability results for the hyper DAG, extending the typical Markov equivalence classes. We next provide insights into why learning the more complex hypergraph structure may actually lead to better empirical results. In particular, more restrictive assumptions like CAM correspond to easier-to-learn hyper DAGs and better finite sample complexity. We finally develop an extension of the greedy CAM algorithm which can handle the more complex hyper DAG search space and demonstrate its empirical usefulness in synthetic experiments.

The $1 trillion pay agreement puts Elon Musk on track to become the world's first trillionaire. Tesla shareholders approved a $1 trillion compensation package for CEO Elon Musk, the largest payout ever awarded to a corporate leader. More than 75% of votes were cast in favor of the unprecedented pay plan, the company said Thursday at its annual meeting. The outcome caps a weekslong campaign by the electric vehicle maker's board, its CEO and prominent retail investors to build support. The pay agreement clears a path for Musk, the world's richest person, to become the first ever trillionaire and expand his stake in Tesla to 25% or more over the next decade.

Tesla chief Elon Musk's $1tn pay package has been approved. Tesla chief Elon Musk's $1tn pay package has been approved. Chants of'Elon' erupt after compensation plan approved despite opposition from several high-profile investors Tesla shareholders approved a $1tn compensation plan for CEO Elon Musk on Thursday, awarding the world's richest person what would be the largest corporate payout in history if he meets the goals necessary to receive it. The pay package, which several high-profile investors opposed, demonstrates that shareholders still believe Musk can lead the automaker in an era dominated by robotics and artificial intelligence. The result of the vote was announced at the annual shareholder event in Austin, Texas, with more than 75% of investors voting in favor of the plan.

'They take the pecking that we see all birds doing and take it to the extreme.' Breakthroughs, discoveries, and DIY tips sent every weekday. Woodpeckers really know how to punch above their weight. The woodland birds can attack a tree at about 15 miles per hour with their powerful beaks . To achieve this, woodpeckers essentially turn themselves into hammers, by bracing their head, neck, abdomen, and tail muscles to hold their bodies completely rigid when they pound into wood.

Elon Musk's $1tn pay deal approved by Tesla shareholders Tesla shareholders have approved a record-breaking pay package for boss Elon Musk that could be worth nearly $1tn (£760bn). The unprecedented deal was approved by 75% of Tesla shareholders who cast votes at the firm's annual general meeting on Thursday. The deal requires Musk, who is already the world's richest man, to drastically raise the electric car firm's market value over a period of years. If he meets various targets, he will be rewarded with hundreds of millions of new shares. The scale of the deal is controversial, but the Tesla board argued that Musk might leave the company if it was not approved - and that it could not afford to lose him.

The unprecedented payday will go into full effect by 2035--as long as Tesla hits ambitious financial and production targets. On Thursday, Tesla shareholders approved an unprecedented $1 trillion pay package for CEO Elon Musk . The full compensation plan will go into effect by 2035--assuming the company successfully hits ambitious financial and production targets. If that happens, Musk will also get control of some 25 percent of the business, up from the 12 percent he controls currently. More than 75 percent of Tesla shareholders approved the move in a preliminary vote.

Tesla CEO Elon Musk has scored a resounding victory as shareholders have approved a pay package of as much as $878bn over the next decade, endorsing his vision of morphing the electric vehicle (EV) maker into an AI and robotics juggernaut. Shares of Tesla rose more than 3 percent in after-hours trading after the shareholders voted on Thursday. The proposal was approved with more than 75 percent support. "What we are about to embark upon is not merely a new chapter of the future of Tesla, but a whole new book," he said. "This really is going to be quite the story."

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They're born as tiny'toadlets.' Breakthroughs, discoveries, and DIY tips sent every weekday. A frog's lifecycle is likely one of the earliest bits of science that many of us remember learning. They start as eggs, hatch into tadpoles, and soon grow into the recognizable adult amphibians. While that remains true for the vast majority of the planet's nearly 8,000 known frog species, a handful of the amphibians have evolved a more streamlined reproductive process.