ROTC students at Old Dominion subdued and killed ISIS-linked gunman who left one dead, two wounded after shouting'Allahu Akbar' and opened fire Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Ey up AI! Scientists are teaching artificial intelligence how to understand UK accents and dialects - so, how many of these regional terms do YOU know? Scientists are teaching AI how to understand slang words such as'chuck' and'nowt' so that automated phone lines can understand local callers. Councils across the UK are turning to artificial intelligence to man their phones, helping people with enquiries such as when to put their bins out or how to pay their council tax.

The central objective of empirical asset pricing is to identify firm-level signals that explain the cross-section of expected stock returns--whether through exposure to risk factors or persistent mispricing. The dominant paradigm, grounded in the assumption of self-predictability, asserts that a firm's own characteristics forecast its own returns (see, e.g., Cochrane (2011); Harvey et al. (2016)). Complementing this view is a growing literature on cross-predictability--the idea that the characteristics or returns of one asset can help forecast the returns of others (see, e.g., Lo and MacKinlay (1990); Hou (2007); Cohen and Frazzini (2008); Cohen and Lou (2012); Huang et al. (2021, 2022)). A key mechanism underpinning this phenomenon is the presence of lead-lag effects, whereby price movements or information from one firm precede and predict those of related firms. Such effects can stem from staggered information diffusion, peer influence within industries, supply chain linkages, or correlated trading by institutional investors that induces price pressure across related assets. Despite recent methodological advances in modeling cross-stock predictability, several foundational questions remain unresolved. Chief among them is how a mean-variance investor can analytically integrate multiple predictive signals when returns are interconnected across assets. Equally crucial is developing a framework that jointly captures both the relevance of individual signals and the structure of return spillovers--enhancing portfolio performance while preserving interpretability .

This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where depth is constrained to be less than the number of classes -- a limitation that proves too rigid for complex classification problems. Our extensions improve performance in multi-class settings with unequal variance-covariance structures and nonlinear class separations by allowing more splits and more flexible class groupings in the projection pursuit computation. Proposing algorithmic improvements is straightforward; demonstrating their actual utility is not. We therefore develop two visual diagnostic approaches to verify that the enhancements perform as intended. Using high-dimensional visualization techniques, we examine model fits on benchmark datasets to assess whether the algorithm behaves as theorized. An interactive web application enables users to explore the behavior of both the original and enhanced classifiers under controlled scenarios. The enhancements are implemented in the R package PPtreeExt.

Understanding minimal assumptions that enable learning and generalization is perhaps the central question of learning theory. Several celebrated results in statistical learning theory, such as the VC theorem and Littlestone's characterization of online learnability, establish conditions on the hypothesis class that allow for learning under independent data and adversarial data, respectively. Building upon recent work bridging these extremes, we study sequential decision making under distributional adversaries that can adaptively choose data-generating distributions from a fixed family $U$ and ask when such problems are learnable with sample complexity that behaves like the favorable independent case. We provide a near complete characterization of families $U$ that admit learnability in terms of a notion known as generalized smoothness i.e. a distribution family admits VC-dimension-dependent regret bounds for every finite-VC hypothesis class if and only if it is generalized smooth. Further, we give universal algorithms that achieve low regret under any generalized smooth adversary without explicit knowledge of $U$. Finally, when $U$ is known, we provide refined bounds in terms of a combinatorial parameter, the fragmentation number, that captures how many disjoint regions can carry nontrivial mass under $U$. These results provide a nearly complete understanding of learnability under distributional adversaries. In addition, building upon the surprising connection between online learning and differential privacy, we show that the generalized smoothness also characterizes private learnability under distributional constraints.

Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing procedures for statistical networks based on the principle of maximum entropy (MaxEnt). Our approach formulates a constrained entropy-maximization problem on the space of networks, subject to prescribed structural constraints. The resulting test statistics are defined through the Lagrange multipliers associated with the constrained optimization problem, which, to our knowledge, is novel in the statistical networks literature. We establish consistency in the classical regime where the number of vertices is fixed. We then consider asymptotic regimes in which the graph size grows with the sample size, developing tests for both dense and sparse settings. In the dense case, we analyze exponential random graph models (ERGM) (including the Erdös-Rènyi models), while in the sparse regime our theory applies to Erd{ö}s-R{è}nyi graphs. Our analysis leverages recent advances in nonlinear large deviation theory for random graphs. We further show that the proposed Lagrange-multiplier framework connects naturally to classical score tests for constrained maximum likelihood estimation. The results provide a unified entropy-based framework for network model assessment across diverse growth regimes.

Mobile data technologies use ``actigraphs'' to furnish information on health variables as a function of a subject's movement. The advent of wearable devices and related technologies has propelled the creation of health databases consisting of human movement data to conduct research on mobility patterns and health outcomes. Statistical methods for analyzing high-resolution actigraph data depend on the specific inferential context, but the advent of Artificial Intelligence (AI) frameworks require that the methods be congruent to transfer learning and amortization. This article devises amortized Bayesian inference for actigraph time sheets. We pursue a Bayesian approach to ensure full propagation of uncertainty and its quantification using a hierarchical dynamic linear model. We build our analysis around actigraph data from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study conducted by the Fielding School of Public Health in the University of California, Los Angeles. Apart from achieving probabilistic imputation of actigraph time sheets, we are also able to statistically learn about the time-varying impact of explanatory variables on the magnitude of acceleration (MAG) for a cohort of subjects.

Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Alexander brothers' alleged HIGH SCHOOL gang rape video: Classmates speak out on sick'taking turns' footage... as creepy unseen photos are exposed Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Live Nation executives mocked'stupid' concert-goers in emails where they bragged about how to best rip them off: '$60 for closer grass' NFL superstar Xavier Worthy spills all on Travis Kelce, the Chiefs' struggles... and having Taylor Swift as his No 1 fan Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Nancy Mace throws herself into Iran warzone as she goes rogue on Middle East rescue mission: 'I AM that person' Hidden toxins in kids' treats EXPOSED: Health guru Jillian Michaels' sit-down with Casey DeSantis reveals dangers lurking in popular foods Why are animals picking on Punch the monkey? Scientists have revealed the tragic truth about Punch the monkey - the viral macaque who has stolen the hearts of millions across social media. The seven-month-old Japanese macaque was born at Ichikawa Zoo last year, where he was rejected by his mother. Zookeepers gave him a stuffed orangutan toy, who he quickly formed a bond with - with viral footage showing him clinging to the plushie. Fans were briefly relieved when footage emerged of another macaque grooming and comforting Punch.

Ukraine has responded to a war it didn't start by creating an industry it doesn't want, but could the nation's drone expertise help it rebuild? To learn more, gained exclusive access to the research labs, factories and military training schools behind Ukraine's drones Killhouse Academy, run by the 3rd Assault Brigade, is Ukraine's leading drone-pilot school. The grinding, attritional war between Russia and Ukraine is now entirely dominated by drones. Russia pummels Ukraine with long-range kamikaze aircraft and Ukraine knocks them out of the sky with specialised interceptors. The front line has transitioned from an artillery battle to a first-person-view drone fight, while ground-based robots are increasingly used to deliver ammunition and supplies, launch attacks and evacuate the wounded. As a result, in the four years since Russia's full-scale invasion, Ukraine has created from nothing an entire industry and ecosystem capable of designing, manufacturing and operating a variety of ingenious drones.

Tech's politics push at home and abroad We report from California's Silicon Valley, where billionaires pour money into midterms, and the AI Impact summit, where India pushes back on'AI monopoly' held by US and China This week, we're examining the tech industry's push for influence in two places separated by a time difference of 13 hours and 30 minutes. The first is where tech sees its next big market, the second its home turf. My colleague Robert Booth reports from last week's India AI Impact summit, where tech companies pledged to spend tens of billions in the coming year to build customer bases and datacenters in the subcontinent. Dara Kerr and Lauren Gambino reported from Silicon Valley, where billionaires are marshalling their wealth to influence California's politics at greater levels than they ever have before. Visitors explore the Google pavilion during the AI Impact summit at Bharat Mandapam in New Delhi, India, on 20 February.

We develop a Coordinate Ascent Variational Inference (CAVI) algorithm for Bayesian Mixed Data Sampling (MIDAS) regression with linear weight parameterizations. The model separates impact coeffcients from weighting function parameters through a normalization constraint, creating a bilinear structure that renders generic Hamiltonian Monte Carlo samplers unreliable while preserving conditional conjugacy exploitable by CAVI. Each variational update admits a closed-form solution: Gaussian for regression coefficients and weight parameters, Inverse-Gamma for the error variance. The algorithm propagates uncertainty across blocks through second moments, distinguishing it from naive plug-in approximations. In a Monte Carlo study spanning 21 data-generating configurations with up to 50 predictors, CAVI produces posterior means nearly identical to a block Gibbs sampler benchmark while achieving speedups of 107x to 1,772x (Table 9). Generic automatic differentiation VI (ADVI), by contrast, produces bias 714 times larger while being orders of magnitude slower, confirming the value of model-specific derivations. Weight function parameters maintain excellent calibration (coverage above 92%) across all configurations. Impact coefficient credible intervals exhibit the underdispersion characteristic of mean-field approximations, with coverage declining from 89% to 55% as the number of predictors grows a documented trade-off between speed and interval calibration that structured variational methods can address. An empirical application to realized volatility forecasting on S&P 500 daily returns cofirms that CAVI and Gibbs sampling yield virtually identical point forecasts, with CAVI completing each monthly estimation in under 10 milliseconds.