Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' The death toll from a Russian attack on a passenger train in Ukraine's Kharkiv region on Tuesday rose to six, after the remains of several bodies were recovered from the wreckage, the Kharkiv Regional Prosecutor's Office said on the Telegram messaging app. At least six people were injured in a Russian missile attack on Ukraine's Zaporizhia region, the head of the regional military administration, Ivan Fedorov, said on Telegram.

Meta boss Mark Zuckerberg plans to ramp up spending on artificial intelligence (AI) projects this year, even as other executives warn of a potential bubble in the industry. During a call with financial analysts on Wednesday to discuss the Facebook-owner's 2025 financial results, the company said it expects to spend up to $135bn (£97bn) this year, mostly on infrastructure related to AI. That is nearly twice the $72bn Meta spent last year on AI projects and infrastructure. In the last three years, the technology giant has spent roughly $140bn in an attempt to get ahead of the AI boom. Zuckerberg said on Wednesday that he is expecting 2026 to be the year that AI dramatically changes the way we work.

Candace Owens leaks Erika Kirk phone call: 'It makes my skin crawl' Why I'm more concerned than ever about what Barron Trump is doing behind closed doors: KENNEDY Revealed: Truth behind Barron Trump's dramatic Facetime phone call with'girlfriend' and the British public school-educated MMA fighter who beat her up Kim Kardashian breaks silence on why Prince Harry and Meghan Markle photos were deleted from Kris Jenner's birthday post Nicki Minaj flashes dagger-long nails as she clutches Trump's hand after gushing she's his No. 1 fan Telling detail stitched into Melania's Dior dress that hints at her true ambitions, as the First Lady rings the New York Stock Exchange bell: JANE TIPPETT Hilarious live gaffe on David Muir's World News Tonight that'triggered behind the scenes meltdown' Extraordinary transformation of beloved child star who has'self-canceled' and ditched Hollywood to live off grid in POVERTY as'Catholic extremist' He's the famed Glambot director whose slow-mo videos of celebs go viral. But now, as he's forced to apologize for leaked emails... nasty rumors are swirling'Greedy pig' Harry Styles is shamefully exploiting obsessed women. I know... because it happened to me: LIZ JONES Bruce Willis' wife Emma makes heartbreaking admission about star's dementia battle Julie Newmar, 92, who played Catwoman on TV's Batman in the '60s, looks amazing in rare sighting Woke CNN guest scolded for vicious personal attack on co-panelist Kevin O'Leary Scientists are about to DRILL into the most fragile part of Antarctica's Doomsday Glacier READ MORE: Doomsday Clock ticks forward... taking us closer to annihilation Scientists are about to drill into the most inaccessible and least-understood part of the Thwaites Glacier. Measuring around the same size as Great Britain, this huge mass of ice in West Antarctica is one of the largest and fastest changing glaciers in the world. Worryingly, research has shown that if it collapses, the glacier will cause global sea levels to rise by a whopping 2.1ft (65cm) - plunging entire communities underwater.

We consider the problem of graph matching for a sequence of graphs generated under a time-dependent Markov chain noise model. Our edgelighter error model, a variant of the classical lamplighter random walk, iteratively corrupts the graph $G_0$ with edge-dependent noise, creating a sequence of noisy graph copies $(G_t)$. Much of the graph matching literature is focused on anonymization thresholds in edge-independent noise settings, and we establish novel anonymization thresholds in this edge-dependent noise setting when matching $G_0$ and $G_t$. Moreover, we also compare this anonymization threshold with the mixing properties of the Markov chain noise model. We show that when $G_0$ is drawn from an Erdős-Rényi model, the graph matching anonymization threshold and the mixing time of the edgelighter walk are both of order $Θ(n^2\log n)$. We further demonstrate that for more structured model for $G_0$ (e.g., the Stochastic Block Model), graph matching anonymization can occur in $O(n^α\log n)$ time for some $α<2$, indicating that anonymization can occur before the Markov chain noise model globally mixes. Through extensive simulations, we verify our theoretical bounds in the settings of Erdős-Rényi random graphs and stochastic block model random graphs, and explore our findings on real-world datasets derived from a Facebook friendship network and a European research institution email communication network.

Cluster analysis relates to the task of assigning objects into groups which ideally present some desirable characteristics. When a cluster structure is confined to a subset of the feature space, traditional clustering techniques face unprecedented challenges. We present an information-theoretic framework that overcomes the problems associated with sparse data, allowing for joint feature weighting and clustering. Our proposal constitutes a competitive alternative to existing clustering algorithms for sparse data, as demonstrated through simulations on synthetic data. The effectiveness of our method is established by an application on a real-world genomics data set.

Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with locally-optimized hyperparameters. We derive collapsed Gibbs sampling that analytically marginalizes latent functions for efficient inference, and introduce adaptive concentration parameter scheduling for coarse-to-fine regime discovery. Our acquisition functions decompose uncertainty into intra-regime and inter-regime components. Experiments on synthetic benchmarks and real-world applications, including molecular conformer optimization, virtual screening for drug discovery, and fusion reactor design, demonstrate consistent improvements over state-of-the-art baselines on multi-regime objectives.

Machine learning predictions are increasingly used to supplement incomplete or costly-to-measure outcomes in fields such as biomedical research, environmental science, and social science. However, treating predictions as ground truth introduces bias while ignoring them wastes valuable information. Prediction-Powered Inference (PPI) offers a principled framework that leverages predictions from large unlabeled datasets to improve statistical efficiency while maintaining valid inference through explicit bias correction using a smaller labeled subset. Despite its potential, the growing PPI variants and the subtle distinctions between them have made it challenging for practitioners to determine when and how to apply these methods responsibly. This paper demystifies PPI by synthesizing its theoretical foundations, methodological extensions, connections to existing statistics literature, and diagnostic tools into a unified practical workflow. Using the Mosaiks housing price data, we show that PPI variants produce tighter confidence intervals than complete-case analysis, but that double-dipping, i.e. reusing training data for inference, leads to anti-conservative confidence intervals and coverages. Under missing-not-at-random mechanisms, all methods, including classical inference using only labeled data, yield biased estimates. We provide a decision flowchart linking assumption violations to appropriate PPI variants, a summary table of selective methods, and practical diagnostic strategies for evaluating core assumptions. By framing PPI as a general recipe rather than a single estimator, this work bridges methodological innovation and applied practice, helping researchers responsibly integrate predictions into valid inference.

We study model-agnostic post-hoc calibration methods intended to improve probabilistic predictions in supervised binary classification on real i.i.d. tabular data, with particular emphasis on conformal and Venn-based approaches that provide distribution-free validity guarantees under exchangeability. We benchmark 21 widely used classifiers, including linear models, SVMs, tree ensembles (CatBoost, XGBoost, LightGBM), and modern tabular neural and foundation models, on binary tasks from the TabArena-v0.1 suite using randomized, stratified five-fold cross-validation with a held-out test fold. Five calibrators; Isotonic regression, Platt scaling, Beta calibration, Venn-Abers predictors, and Pearsonify are trained on a separate calibration split and applied to test predictions. Calibration is evaluated using proper scoring rules (log-loss and Brier score) and diagnostic measures (Spiegelhalter's Z, ECE, and ECI), alongside discrimination (AUC-ROC) and standard classification metrics. Across tasks and architectures, Venn-Abers predictors achieve the largest average reductions in log-loss, followed closely by Beta calibration, while Platt scaling exhibits weaker and less consistent effects. Beta calibration improves log-loss most frequently across tasks, whereas Venn-Abers displays fewer instances of extreme degradation and slightly more instances of extreme improvement. Importantly, we find that commonly used calibration procedures, most notably Platt scaling and isotonic regression, can systematically degrade proper scoring performance for strong modern tabular models. Overall classification performance is often preserved, but calibration effects vary substantially across datasets and architectures, and no method dominates uniformly. In expectation, all methods except Pearsonify slightly increase accuracy, but the effect is marginal, with the largest expected gain about 0.008%.

Machine learning models in high-stakes applications, such as recidivism prediction and automated personnel selection, often exhibit systematic performance disparities across sensitive subpopulations, raising critical concerns regarding algorithmic bias. Fairness auditing addresses these risks through two primary functions: certification, which verifies adherence to fairness constraints; and flagging, which isolates specific demographic groups experiencing disparate treatment. However, existing auditing techniques are frequently limited by restrictive distributional assumptions or prohibitive computational overhead. We propose a novel empirical likelihood-based (EL) framework that constructs robust statistical measures for model performance disparities. Unlike traditional methods, our approach is non-parametric; the proposed disparity statistics follow asymptotically chi-square or mixed chi-square distributions, ensuring valid inference without assuming underlying data distributions. This framework uses a constrained optimization profile that admits stable numerical solutions, facilitating both large-scale certification and efficient subpopulation discovery. Empirically, the EL methods outperform bootstrap-based approaches, yielding coverage rates closer to nominal levels while reducing computational latency by several orders of magnitude. We demonstrate the practical utility of this framework on the COMPAS dataset, where it successfully flags intersectional biases, specifically identifying a significantly higher positive prediction rate for African-American males under 25 and a systemic under-prediction for Caucasian females relative to the population mean.

Survival analysis has become a standard approach for modelling time to default by time-varying covariates in credit risk. Unlike most existing methods that implicitly assume a stationary data-generating process, in practise, mortgage portfolios are exposed to various forms of data drift caused by changing borrower behaviour, macroeconomic conditions, policy regimes and so on. This study investigates the impact of data drift on survival-based credit risk models and proposes a dynamic joint modelling framework to improve robustness under non-stationary environments. The proposed model integrates a longitudinal behavioural marker derived from balance dynamics with a discrete-time hazard formulation, combined with landmark one-hot encoding and isotonic calibration. Three types of data drift (sudden, incremental and recurring) are simulated and analysed on mortgage loan datasets from Freddie Mac. Experiments and corresponding evidence show that the proposed landmark-based joint model consistently outperforms classical survival models, tree-based drift-adaptive learners and gradient boosting methods in terms of discrimination and calibration across all drift scenarios, which confirms the superiority of our model design.