Trump's stunning Georgia silence gifts America's'most endangered Democrat' Jon Ossoff a vital lifeline Ugly behind-the-scenes reality of Blake Lively's'paradise' compound: Unpaid workers, a $2MILLION debt... and humiliating new question she and Ryan Reynolds must now face Hidden warning signs you are taking the WRONG dose of Ozempic: Doctor sounds alarm over dangerous mistake... and reveals four lifestyle tweaks to avoid horror side effects'Beloved' college basketball player tragically killed in hit-and-run accident Inside Meryl Streep's very secret relationship with Martin Short: Friends finally reveal how pair bonded through trauma... incredible measures they take to hide the truth... and why there is'no doubt they are in love' Trumpworld's new eyebrow-raising addiction that even health boss RFK Jr admits to using daily Young American women in the crosshairs of dark network: They flirt and flatter, watching every move... then they strike The Chicks' Natalie Maines delivers foul-mouthed Trump rant 23 years after famously slamming George W. Bush Fast-food chain struggles under California's soaring minimum wage as frightened staff abandon crime-ridden locations Middle-aged male school board member faces criminal charges after flirting with teenage girl at public meeting: 'God, you're hot' Michelle Obama says same'anger' that led to husband's presidential victory is fueling Trump's MAGA movement: 'Those folks are drowning' Hero Amazon delivery driver jumps to woman's defense and saved her life during horror hammer attack at her home San Diego mosque shooters hated EVERYONE, according to manifesto being combed by FBI after massacre, as killer teen's $1m home is raided by cops Why Taylor Swift has cut out Travis Kelce's father ahead of wedding: He'cannot be trusted', say insiders... as'f***ed up' Blake Lively drama and preposterous demands leak out An alien invasion might sound like science fiction, but a scientist has now revealed what the terrifying consequences of an encounter might be. Professor Avi Loeb, head of Harvard University's Galileo Project, claims our first encounter with an alien invader won't resemble sci-fi movies like E.T or War of the Worlds. Rather than a biological, flesh and blood alien, Professor Loeb explains that we are more likely to be met by a'technological device guided by AI '. The arrival of such a device would pose a'potential threat to all earthlings', he claims - sparking political, economic, and spiritual chaos around the world. Professor Loeb told the Daily Mail that'the stock market may crash due to the uncertainty about the impact of the encounter on the future of humanity.'

Ukrainian mid-range strikes deal double blow to Russia's war effort KYIV/LONDON - From burning oil refineries to a stalling ground offensive, Russia is suffering problems in its war against Ukraine that partly stem from a growing Ukrainian military strength: the use of medium-range drone attacks. By targeting Russian air defenses and logistics dozens of kilometers behind front lines, Ukraine is disrupting Russia's battlefield advances and opening the way for long-range strikes on Russian oil and military facilities, said two Ukrainian commanders, two drone specialists and three military analysts. Ukrainian officials say more resources have in recent months been poured into "middle strikes," typically ranging between 30 kilometers and 180 km behind front lines. 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.

U.S. seeking transfer of intellectual property rights in drone deal, Kyiv says Through a combination of new technology and tactics, Kyiv's forces have been able to strike deep into Russian territory, to slow and in some cases even reverse battlefield gains by Moscow's bigger army and inflict significant damage on oil facilities that help finance the Kremlin's war machine. Kyiv has said that the U.S. is seeking the transfer of technology and access to intellectual property rights from Ukraine as part of a drone deal that is awaiting approval at the highest political level, a person familiar with the matter has said. The U.S. Department of Defense has asked to test a range of Ukrainian defense products, including drones and electronic warfare systems, as Washington is considering their potential purchase for military use, the official said. The agreement has not been finalized, the person added, speaking on condition of anonymity because the discussions are private. Growing interest from the U.S. shows how the world's largest military is looking to tap into the drone expertise Ukraine has acquired over four years fighting against the Russian invasion.

The main XAI attribution methods for deep neural networks -- GradCAM, SHAP, LIME, Integrated Gradients -- operate on separate theoretical foundations and are not formally comparable. We present GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley), a mathematical framework establishing a representation theory for attributions: every additive, linear, and continuous attribution functional on L^2(Q,mu) admits a unique canonical representation (Q, w, Delta), proved necessary by the Riesz Representation Theorem. This class encompasses SHAP, IG, LIME and linearized GradCAM, but excludes nonlinear functionals such as standard GradCAM or attention maps. Seven formal theorems provide simultaneous guarantees absent in any individual method: (T1) necessary canonical form; (T2) exact completeness; (T3) Monte Carlo convergence O(1/sqrt(m))+O(1/k); (T4) exact Shapley Interaction Values; (T5) Hoeffding ANOVA decomposition; (T6) Sobol sensitivity generalization; (T7) multi-scale extension (MS-GRALIS) with minimum-variance weights. An algebraic appendix justifies the GRALIS-SIV correspondence via the Mobius transform without circularity. GRALIS satisfies 13.5/14 axiomatic properties vs. 2.5-6/14 for individual methods, including completeness, sensitivity, locality, order-k interactions and optimal multi-scale aggregation simultaneously. Preliminary validation on BreaKHis (1,187 histology images, DenseNet-121) reports deletion faithfulness AUC +0.015 (malignant), 96% class-conditional consistency, SAL = 0.762+/-0.109 and sparsity index 0.39. Extended comparison with baseline XAI methods is planned for a companion paper.

Given an observation $\mathbf Y \in \mathbb{R}^{d_1\times d_2}$ from the model $\mathbf Y = \mathbf X + \mathbf E$ where $\mathbf X$ is constant and $\mathbf E$ has i.i.d. $N(0,1)$ entries, we consider the problem of detecting a planted submatrix in the mean matrix $\mathbf X$. Specifically, we aim to distinguish the null hypothesis $\mathbf X = 0$ from the alternative hypothesis in which $\mathbf X$ is non-zero only on a submatrix of size $s_1 \times s_2$ with elevated entries bounded below by $μ>0$. We establish a minimax lower bound characterizing how large $μ$ must be to ensure that the two hypotheses are distinguishable with high probability. Furthermore, we derive novel minimax-optimal tests achieving the lower bound, and describe extensions of these tests that are adaptive to unknown sparsity levels $s_1$ and $s_2$. In contrast with previous work, which required restrictive assumptions on $s_1,s_2, d_1$ and $d_2$, our non-asymptotic upper and lower bounds match for any configuration of these parameters.

We propose non-parametric estimators for the average run length (ARL) and average detection delay (ADD) in quickest changepoint detection (QCD) under finite and irregular sequence lengths. Although ARL and ADD are widely used as optimality criteria in theoretical and simulation studies, their application to real-world datasets is hindered by limited and irregular sequence lengths. To address this issue, we propose non-parametric estimators for the ARL and ADD, termed KM-ARL and KM-ADD, by drawing an analogy between QCD and survival analysis to model detection probabilities under sequence truncation. We derive estimation bias bounds and prove that they are asymptotically unbiased unless extrapolation is required. Experiments on simulated and real-world datasets demonstrate their practical utility, enhancing robustness against limited and irregular sequence lengths, improving interpretability, and facilitating empirical, intuitive model selection. Our Python code is provided at https://github.com/TaikiMiyagawa/Kaplan-Meier-Average-Run-Length, offering ready-to-use implementations for practitioners.

A natural assumption is that if each model is individually calibrated, the aggregate prediction will also be well calibrated. We show that this assumption fails in multi-agent settings: individually calibrated predictors can become collectively miscalibrated when their predictions interact strategically--where "strategically" refers to the game-theoretic sense of Brier-optimal local response, not deliberate gaming or collusion, and arises naturally whenever agents are independently trained on overlapping data. This phenomenon affects multiple independent agents in federated healthcare, multi-vendor intrusion detection, and crowdsourced forecasting, where agents optimize their own objectives. Specifically, we prove that under Brier-score-based aggregation with positively correlated beliefs each agent's individually optimal report systematically underestimates the positive-class probability, yielding a Price of Anarchy strictly greater than one whenever Cov(bi,bj) > 0. At our canonical setting (n=5 agents, pairwise correlation ρ=0.5, base rate µ=0.3, threshold τ=0.3) the empirically measured PoA in false-negative rate is 7.25 (mean aggregate bias 0.375). In contrast, VCG-based aggregation, which rewards each agent's marginal contribution to aggregate accuracy, achieves dominant-strategy incentive compatibility and the lowest empirical PoA among all mechanisms studied (PoA 1.0). On three real-world datasets (NSL-KDD, UNSW-NB15, Credit Card Fraud) with featurepartitioned agents, VCG provides the strongest robustness guarantees among the aggregation methods we evaluate, while maintaining comparable accuracy. In data-sparse regimes (n 500), VCG consistently outperforms stacking and majority voting; under adversarial agents, VCG maintains substantially lower false-negative rates than robust aggregation baselines. Adaptive weight updates further reduce false negatives by 20-22% under distribution shift, with O( T) online regret guarantees. These results establish that how probabilistic predictions are aggregated matters as much as how well individual models are calibrated.

Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and structural anomalies that break standard metric properties. We show that such misspecification pushes the data-generating distribution outside the model class, causing Bayesian inference to become overconfident and poorly calibrated. To address this, we propose a generalized posterior framework for random geometric graphs. We introduce Link-Sequential R-SafeBayes, a method that exploits dyadic conditional independence to estimate prequential risk and adaptively tune posterior regularization. Experiments on synthetic and real-world networks demonstrate improved calibration, better link prediction performance, and a reliable criterion for selecting latent geometries across Euclidean, spherical, and hyperbolic spaces.

Heavy-tailed distributions are prevalent in performance evaluation, network traffic, and risk modeling. This behavior poses a fundamental challenge for modern deep generative models. Standard Variational Autoencoders (VAEs) employ Gaussian decoder likelihoods and Lipschitz-constrained neural networks, a combination that is structurally incapable of producing heavy-tailed outputs: the Gaussian tail decays exponentially, and Lipschitz continuity prevents the decoder from amplifying rare events from the latent space input to sufficiently overcome this decay. We provide both a theoretical characterization of this limitation and a controlled empirical demonstration using synthetic Pareto data across a grid of tail indices $α$ $\in$ {2, 3, 5, 30} and dimensions d $\in$ {1, 5, 10}. As a solution, we replace the Gaussian decoder with a Phase-Type (PH) distribution based on Markov chains, while keeping the encoder, latent space, and training procedure identical. PH distributions allow for arbitrarily precise approximations of any positive-valued distributions, including heavy-tailed families. Experiments showed that the PH-based model reduces tail Kolmogorov-Smirnov distance by up to x6 and extreme quantile error by up to x10 compared to the Gaussian baseline for heavy-tailed data. These results demonstrate that integrating Markov chain-based distributions into the decoder of a generative model institutes a principled and practically effective solution to the heavy-tail generation problem.

Unobserved confounding is a fundamental challenge for estimating causal effects. To address unobserved confounding, recent literature has turned to two different approaches -- proxy variables and the use of multiple treatments. The first approach, commonly referred to as proximal causal inference, requires proxies to be assigned to specific asymmetric roles: treatment-inducing proxies (negative control exposures), variables that act as common causes of the treatment and outcome, and outcome-inducing proxies (negative control outcomes). In practice, however, identifying variables that satisfy these asymmetric roles can be difficult depending on the application domain. The second approach, commonly referred to as the ``Deconfounder," deals with multiple conditionally independent treatments. There has been limited progress towards developing a consistent estimation method for this setting. As the primary contribution of this work, we establish that causal effects are identifiable in both settings when the unobserved confounder is categorical under suitable conditions. Our approach builds on a mixture learning perspective: we show that the underlying confounding structure can be recovered by identifying the corresponding mixture distribution. We propose an estimation procedure based on tensor decomposition, which allows consistent recovery of the latent structure and comes with non-asymptotic guarantees. Simulation studies and real data experiments demonstrate that the proposed method performs well even with limited data.