We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are linearly independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and derive the associated limiting distribution. A consistent estimator of the asymptotic variance is also provided, which plays a key role in the related inference problems. All results are validated through extensive simulations and two real data applications.

This paper proposes a collapsible method for estimating causal effects that maintains the estimator's consistency before and after marginalization over some variables in completed partially directed acyclic graphs (CPDAGs). We first introduce the estimate collapsibility for CPDAGs and characterize the minimal collapsible sets as strong d-convex hulls. An efficient algorithm is devised to obtain such sets in DAGs and is generalized to CPDAGs. Then, we combine the graph reduction procedure with the IDA framework.

We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.

Muon replaces a matrix gradient $G=UΣV^\top$ by its polar factor $UV^\top$. This keeps the singular directions selected by the gradient, but makes the update spectrum flat. We study the optimization bias created by this operation. Under explicit alignment assumptions, we prove that the polar update is the one-step entropy-maximizing choice among bounded updates that use the gradient singular directions and do not adapt to the current weight spectrum. In an underdetermined regression model, we derive exact singular-value dynamics for continuous-time Muon and identify a measurement-dependent condition under which the normalized spectrum moves toward equal nonzero singular values. This geometry also rules out a common low-rank interpretation: at fixed Frobenius norm, Muon's distinguished state has a flat spectrum, whereas nuclear-norm minimization favors spectral concentration. Controlled matrix-sensing experiments separate the effect from simple gradient rescaling, show that norm-matched gradient descent does not reproduce Muon, and recover the predicted flattening trend across broad ablations. In small NanoGPT pretraining, Muon preserves stable rank, has a broad learning-rate plateau, and improves validation loss relative to AdamW; in a matched small-ViT control, the ranking reverses. The resulting picture is regime-dependent: Muon is not universally superior, but its flat-spectrum bias can help when many spectral directions need to remain active.

Accurate vessel traffic flow prediction is crucial for smart port operations and navigational safety. However, maritime traffic flow data are often highly sparse with intermittent bursts, making robust forecasting challenging. Under such conditions, conventional spatio-temporal graph neural networks (ST-GNNs) can degrade toward conservative near-zero predictions and fail to capture non-zero activity. Although zero-inflated negative binomial (ZINB) models partially address excess zeros, their two-part formulation can still remain conservative around abrupt transitions. To address these issues, we propose a model-agnostic learnable Tweedie head that can be attached as a plug-and-play output module to arbitrary ST-GNN backbones. Instead of likelihood-based Tweedie training, which typically requires surrogate objectives, our approach optimizes the closed-form Tweedie unit deviance and predicts the mean for point forecasting while learning a node-level variance power to capture heterogeneous variability across port areas. Experiments on a maritime traffic graph constructed from real-world AIS data in the Port of Los Angeles and Long Beach show that the proposed head consistently improves RMSE across multiple ST-GNN backbones, especially on non-zero events, leading to more reliable forecasts for practical maritime traffic control.

Performative prediction studies feedback loops that arise when predictive models are deployed in consequential domains. In these settings, deploying a model can change the population whose patterns the model aims to predict, inducing a distribution shift that is endogenous to the learning system. This perspective departs from classical treatments of distribution shift, where shifts are typically modeled as exogenous changes in the data-generating process. Yet, in practice, distribution shift is rarely one or the other. Predictive models may influence future data through the decisions they support, while the world itself continues to drift for reasons beyond the learner's control. We study partially performative prediction, a framework that captures both endogenous and exogenous sources of distribution shift. The framework generalizes performative prediction by allowing the data distribution to evolve both in response to the deployed model and according to an external, time-varying process. We extend the central notions of performative stability and performative optimality to this setting by defining their online analogues that track the evolving partially performative environment. We analyze practical learning heuristics, including repeated retraining, and characterize when they successfully adapt to partially performative environments.

SpaceX's stock market blast-off could be Musk's biggest gamble yet It's 07:25 am, 13 October 2024, at Starbase, near Boca Chica on the Texas side of the US/Mexico border, and on the launch pad stands the biggest rocket ever made. Its engines fire and it climbs into the skies over the Gulf of Mexico to cheers and screams in the SpaceX control room. But the launch is not the main event. What goes up must come down - and how it comes down will become a milestone in space exploration. Seven minutes later, the massive rocket booster that blasted the craft towards space starts falling back to Earth - until its engines reignite as planned.

Could humanoid robots be heading for the battlefield? I've come to an industrial space in a tech-heavy area of San Francisco expecting to see a menacing humanoid robot solider doing something combat-like: the future of land-based warfare, perhaps. Instead, the black shiny faceless Phantom robot is engaged in free play, manipulating a bunch of coloured kids blocks. We need data from it just interacting with its environment [and] this is today's menu, explains Sankaet Pathak, co-founder and CEO of two-year-old start-up Foundation Robotics, which is developing Phantom for military and civilian applications. Later he pushes its 80kg steel-covered body around the room to demonstrate its stability and shows me how it walks.

Caitlyn Jenner biographer and Robin Riker's ex William Hasley found dead on hiking trail at 78 Karmelo Anthony's mother sobs with shock as son is found guilty of murdering Austin Metcalf, 17, in stabbing that horrified America: Live updates 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 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' Urgent recall for 1.1m vehicles over fears they could spontaneously CATCH FIRE even when parked 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. 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 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 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 A strong earthquake that struck the Gulf of America on Monday, sending shockwaves hundreds of miles away into Florida. A 6.1 magnitude was detected west-northwest of Mantua, Cuba, with shaking reported as far north as Tallahassee.

The'disappearing into the bushes like Homer Simpson' strategy is a bold choice. Only a day after a dormant bit of code that seemed to be a facial recognition algorithm was discovered in a companion app for its smart glasses, Meta released an update which removed that code, Wired reported. The publication had first uncovered the suspicious code, internally dubbed Name Tag within Meta, while reviewing code for a Meta AI app which handles some core features of the glasses. In other words, the same app necessary for pairing Meta smart glasses to a user's phone over Bluetooth was also ready to start harvesting every face a user passed by while wearing them. It contained algorithms which would have converted photos of faces into biometric identifiers stored on-device and cross referenced with each new facial scan.