More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Hurricane Edouard as seen from the International Space Station in 2014. Breakthroughs, discoveries, and DIY tips sent six days a week. More signs indicate the 2026 Atlantic hurricane season could ultimately be a welcome reprieve from more recent devastating storms . As La Niña transitions into a stronger El Niño climate pattern later this summer, the United States may experience a below-average number of hurricanes.

From recipe changes to aging taste buds, here's why those peanut butter cups don't hit like they used to. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. There's a reason you might remember Hershey's chocolate differently. Breakthroughs, discoveries, and DIY tips sent six days a week. Brad Reese, grandson of Reese's Peanut Butter Cups inventor H.B. Reese, caused a stir this year with his claims that The Hershey Company had changed his grandfather's recipes beyond recognition .

Vance grounded at White House as Iran peace talks in turmoil and Trump declares: 'I expect to be bombing' New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Ark of the Covenant's final resting place pinpointed by archaeologists as fresh search begins Ritzy Bay Area town torn apart after teacher's daughter, 16, crashed car while speeding and killed four friends... then posted a TikTok video that poured fuel on the flames Jordon Hudson extends her control over Bill Belichick's empire with secret move that is set to leave his family and friends furious Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' AMANDA PLATELL: Why Sarah Ferguson - with the ghost of Princess Diana at her side - is ready to sensationally blow up the Royal Family. She knows ALL their secrets... Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran Sydney Sweeney's role is cut from The Devil Wears Prada 2 Humiliating moment runner celebrates winning marathon... only to be pipped at the line by rival in brutal finish Patriots coach Mike Vrabel reveals'difficult conversations' with his wife as he speaks out for the first time since Dianna Russini photo scandal Nancy Mace fires back after accused sexual extorter Cory Mills tries to expel her from Congress: 'Bring it on' How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. The new'posh' drug that's easier to order than Uber Eats - and why all my middle-class friends have ditched booze and cocaine for it: JANA HOCKING Grieving mother says she went to LA school every day to complain daughter was being bullied... then tragedy struck when the lead tormentor, 12, hurled metal water bottle at victim's head Autistic woman, 24, worked hard to build independent life for herself... now she's PARALYZED thanks to selfishness of stranger READ MORE: Conjoined twin'influencers' are revealed to be AI AI influencers are cashing in on Coachella, with some set to make tens of thousands from their content. Among the celebrities and content creators, you may have noticed a surge in festival content from digital influencers.

Ritzy Bay Area town torn apart after teacher's daughter, 16, was behind wheel when four friends died in high-speed crash... then she posted a TikTok video that poured fuel on the flames Two CIA officers killed in Mexico when their car skidded off ravine and exploded after meeting about bust of'largest ever drug lab' Insiders claim failed AI rollout could be to blame for Tim Cook's departure from Apple - as one says'the AI era requires a different kind of leadership' Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' Fury as murderer marries pen pal behind bars... as teenage victim's mom says: 'I'm serving a life sentence without my son' Kate and William join Charles and Camilla in celebrating British centenarians at Buckingham Palace as Royal Family marks the late Queen's 100th birthday US troops board second tanker as Trump accuses Iran of violating ceasefire'numerous times' - Live updates AMANDA PLATELL: Why Sarah Ferguson - with the ghost of Princess Diana at her side - is ready to sensationally blow up the Royal Family. She knows ALL their secrets... Team USA Olympics star Noah Lyles slammed for'horrible' reaction to his wife's wedding dress reveal How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. I was losing hair so fast a bald spot the size of an orange appeared. I owe my life to a $1 at-home treatment that REVERSED the damage in a month.

Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE methods are usually efficient at inference time, yet their performance can seriously deteriorate when the discrepancy between distributions is large. In contrast, score-based DRE methods often yield more accurate estimates in such settings, but they typically require considerable repeated function evaluations and numerical integration. We propose One-step Score-based Density Ratio Estimation (OS-DRE), a partly analytic and solver-free framework designed to combine these complementary advantages. OS-DRE decomposes the time score into spatial and temporal components, representing the latter with an analytic radial basis function (RBF) frame. This formulation converts the otherwise intractable temporal integral into a closed-form weighted sum, thereby removing the need for numerical solvers and enabling DRE with only one function evaluation. We further analyze approximation conditions for the analytic frame, and establish approximation error bounds for both finitely and infinitely smooth temporal kernels, grounding the framework in existing approximation theory. Experiments across density estimation, continual Kullback-Leibler and mutual information estimation, and near out-of-distribution detection demonstrate that OS-DRE offers a favorable balance between estimation quality and inference efficiency.

We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$. For $L$-smooth convex loss, we provide fully-adaptive algorithms achieving regret of order $\widetilde{O}(\|u\|\sqrt{V_T(u)} + L\|u\|^2+G^4)$ without requiring prior knowledge of comparator norm $\|u\|$, Lipschitz constant $G$, or smoothness $L$. The update in each round can be computed efficiently via a closed-form expression. Our results extend to dynamic regret and find immediate implications to the stochastically-extended adversarial (SEA) model, which significantly improves upon the previous best-known result [Wang et al., 2025].

Classical information-theoretic generalization bounds typically control the generalization gap through KL-based mutual information and therefore rely on boundedness or sub-Gaussian tails via the moment generating function (MGF). In many modern pipelines, such as robust learning, RLHF, and stochastic optimization, losses and rewards can be heavy-tailed, and MGFs may not exist, rendering KL-based tools ineffective. We develop a tail-dependent information-theoretic framework for sub-Weibull data, where the tail parameter $θ$ controls the tail heaviness: $θ=2$ corresponds to sub-Gaussian, $θ=1$ to sub-exponential, and $0<θ<1$ to genuinely heavy tails. Our key technical ingredient is a decorrelation lemma that bounds change-of-measure expectations using a shifted-log $f_θ$-divergence, which admits explicit comparisons to Rényi divergence without MGF arguments. On the empirical-process side, we establish sharp maximal inequalities and a Dudley-type chaining bound for sub-Weibull processes with tail index $θ$, with complexity scaling as $\log^{1/θ}$ and entropy$^{1/θ}$. These tools yield expected and high-probability PAC-Bayes generalization bounds, as well as an information-theoretic chaining inequality based on multiscale Rényi mutual information. We illustrate the consequences in Rényi-regularized RLHF under heavy-tailed rewards and in stochastic gradient Langevin dynamics with heavy-tailed gradient noise.

We consider the problem of clustering nested or hierarchical data, where observations are grouped and there are both group-level and observation-level variables. In our motivating OneK1K dataset, observations consist of single-cell RNA-sequencing (scRNA-seq) data from 982 individuals (groups), totaling 1.27 million cells (observations), along with individual-specific genotype data. This type of data would enable the identification of cell types and the investigation of how genetic variations among individuals influence differences in cell-type profiles. Our goal, therefore, is to jointly cluster cells and individuals to capture the heterogeneity across both levels using cell-specific gene expressions as well as individual-specific genotypes. However, existing grouped clustering methods do not incorporate group-level variables, thereby limiting their ability to capture the heterogeneity of genotypes in our motivating application. To address this, we propose the Nested Atoms Model (NAM), a new Bayesian nonparametric approach that enables the desired two-layered clustering, accounting for both group-level and observation-level variables. To scale NAM for high-dimensional data, we develop a fast variational Bayesian inference algorithm. Simulations show that NAM outperforms existing methods that ignore group-level variables. Applied to the OneK1K dataset, NAM identifies clusters of genetically similar individuals with homogeneous cell-type profiles. The resulting cell clusters align with known immune cell types based on differential gene expression, underscoring the ability of NAM to capture nested heterogeneity and provide biologically meaningful insights.

We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via weights assigned to each sample, to obtain weighted versions of standard estimators such as M-estimators and maximum-likelihood estimators. Under mild assumptions on the data, we obtain a precise asymptotic characterization of the performance of our method for general Gaussian designs, in the high-dimensional limit where the number of samples and covariate dimension grow proportionally. We show how this characterization can be used to efficiently construct a posterior distribution over change points. Numerical experiments on both simulated and real data illustrate the efficacy of Weighted ERM compared to existing approaches, demonstrating that sample weights constructed with weakly informative priors can yield accurate change point estimators. Our method is implemented as an open-source package, weightederm, available in Python and R.

Preprocessing leakage arises when scaling, imputation, or other data-dependent transformations are estimated before resampling, inflating apparent performance while remaining hard to detect. We present fastml, an R package that provides a single-call interface for leakage-aware machine learning through guarded resampling, where preprocessing is re-estimated inside each resample and applied to the corresponding assessment data. The package supports grouped and time-ordered resampling, blocks high-risk configurations, audits recipes for external dependencies, and includes sandboxed execution and integrated model explanation. We evaluate fastml with a Monte Carlo simulation contrasting global and fold-local normalization, a usability comparison with tidymodels under matched specifications, and survival benchmarks across datasets of different sizes. The simulation demonstrates that global preprocessing substantially inflates apparent performance relative to guarded resampling. fastml matched held-out performance obtained with tidymodels while reducing workflow orchestration, and it supported consistent benchmarking of multiple survival model classes through a unified interface.