Daycare accused of multimillion-dollar fraud shifts blame for'revealing' mistake above its front door... as kids are suddenly'trucked in' Pilot best friends die after their helicopters collided in mid-air just after they'd eaten breakfast together at local cafe Everyone's getting sacked': An electrifying phone call, spiralling costs and a troubling'transition'... as Harry and Meghan's most loyal aide leaves, insiders tell ALISON BOSHOFF what's really going on behind the scenes I was told my weight gain, facial hair and fatigue were normal. The mob used Marilyn Monroe as bait to blackmail the Kennedys. And when it didn't work she was murdered... in the most obscene way George Clooney, wife Amal and their eight-year-old twins become French citizens despite the actor admitting he's'bad' at speaking the language Blonde-haired teenage girl reveals what she thinks of Elon Musk's'creepy' public lust for her US strikes'terrorist boat' lurking in international waters as dramatic footage shows devastating moment of impact I shed a staggering 100lbs WITHOUT Ozempic: How I conquered my'out of control' eating habits to transform my life with a simple change Grim details of how shark lover's body was identified after she was killed by one of the predators while swimming off California coast Health and wellness expert reveals the fitness trend of 2026... 'Zone Zero exercise will be essential' Fears Anthony Joshua's car crash injuries are worse than first thought: Sources say £100m Tyson Fury mega-fight is in the balance amid potential internal injuries and psychological trauma of seeing close friends killed Joe Rogan slammed for'pretty girl' comment about champion fighter Dakota Ditcheva A Boy Scout vanished in the mountains then stumbled into a police station 12 years later. The tale gripped social media... but then the truth came out Inside the somber birthday of Rob Reiner's heartbroken daughter Romy: Pictured for first time since parents' murders... she seeks solace at the beach with boyfriend and family by her side Promising young graduate, 23, was coaxed into suicide by ChatGPT'friend', distraught parents allege David Muir's stunning $7m lakeside retreat revealed... as locals in cozy town where ABC News star can be himself offer intriguing glimpses into his private life A snapshot of the universe at work: Incredible image shows'star-making factory' inside a Large Magellanic Cloud A new picture from NASA's Hubble Space Telescope has revealed a beautiful'star-making factory' deep in the universe this week. The image focuses in on a piece of space 160,000 light years from Earth in the Large Magellanic Cloud.

SoftBank Group aims to capitalize on soaring demand for the computing capacity that underpins artificial intelligence applications. SoftBank Group agreed to buy private equity firm DigitalBridge Group for about $3 billion in cash, part of the Japanese conglomerate's push to invest in data centers and other digital infrastructure fueling the artificial intelligence boom. SoftBank will pay $16 per share for New York-listed DigitalBridge, the companies said in statement Monday, confirming an earlier Bloomberg News report. The offer -- valued at $4 billion, including debt -- is a 65% premium to DigitalBridge's closing share price on Dec. 4, the last trading day before talks between the two companies were reported. SoftBank's billionaire founder Masayoshi Son aims to capitalize on soaring demand for digital infrastructure, driven by the AI boom.

Music in 2026: Who's releasing new albums and will Oasis play Knebworth? As the sun sets on 2025, all the year-end lists have been published and it's time to look forward to what 2026 has in store. In many ways, the last 12 months have felt transitional. With relatively few A-list releases, and a Brat-shaped hole in the summer, music seemed to split in two. The charts were agonisingly static: Just three songs held the number one spot hostage for half the year: Taylor Swift's Fate of Ophelia, Huntr/x's Golden, and Alex Warren's Ordinary (never has a song been so aptly titled).

We present an online method for guaranteeing calibration of quantile forecasts at multiple quantile levels simultaneously. A sequence of $α$-level quantile forecasts is calibrated if the forecasts are larger than the target value at an $α$-fraction of time steps. We introduce a lightweight method called Multi-Level Quantile Tracker (MultiQT) that wraps around any existing point or quantile forecaster to produce corrected forecasts guaranteed to achieve calibration, even against adversarial distribution shifts, while ensuring that the forecasts are ordered -- e.g., the 0.5-level quantile forecast is never larger than the 0.6-level forecast. Furthermore, the method comes with a no-regret guarantee that implies it will not worsen the performance of an existing forecaster, asymptotically, with respect to the quantile loss. In experiments, we find that MultiQT significantly improves the calibration of real forecasters in epidemic and energy forecasting problems.

We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly parameterized CDEs act as continuous-time reservoirs, mapping input paths to rich representations. Only a linear readout layer is trained, resulting in fast, scalable models with strong inductive bias. Building on this foundation, we propose two variants: (i) Random Fourier CDEs (RF-CDEs): these lift the input signal using random Fourier features prior to the dynamics, providing a kernel-free approximation of RBF-enhanced sequence models; (ii) Random Rough DEs (R-RDEs): these operate directly on rough-path inputs via a log-ODE discretization, using log-signatures to capture higher-order temporal interactions while remaining stable and efficient. We prove that in the infinite-width limit, these model induces the RBF-lifted signature kernel and the rough signature kernel, respectively, offering a unified perspective on random-feature reservoirs, continuous-time deep architectures, and path-signature theory. We evaluate both models across a range of time-series benchmarks, demonstrating competitive or state-of-the-art performance. These methods provide a practical alternative to explicit signature computations, retaining their inductive bias while benefiting from the efficiency of random features.

Distribution shift is the defining challenge of real-world machine learning. The dominant paradigm--Unsupervised Domain Adaptation (UDA)--enforces feature invariance, aligning source and target representations via symmetric divergence minimization [Ganin et al., 2016]. We demonstrate that this approach is fundamentally flawed: when domains are unequally informative (e.g., high-quality vs degraded sensors), strict invariance necessitates information destruction, causing "negative transfer" that can be catastrophic in safety-critical applications [Wang et al., 2019]. We propose a decision-theoretic framework grounded in Le Cam's theory of statistical experiments [Le Cam, 1986], using constructive approximations to replace symmetric invariance with directional simulability. We introduce Le Cam Distortion, quantified by the Deficiency Distance $δ(E_1, E_2)$, as a rigorous upper bound for transfer risk conditional on simulability. Our framework enables transfer without source degradation by learning a kernel that simulates the target from the source. Across five experiments (genomics, vision, reinforcement learning), Le Cam Distortion achieves: (1) near-perfect frequency estimation in HLA genomics (correlation $r=0.999$, matching classical methods), (2) zero source utility loss in CIFAR-10 image classification (81.2% accuracy preserved vs 34.7% drop for CycleGAN), and (3) safe policy transfer in RL control where invariance-based methods suffer catastrophic collapse. Le Cam Distortion provides the first principled framework for risk-controlled transfer learning in domains where negative transfer is unacceptable: medical imaging, autonomous systems, and precision medicine.

We investigate machine learning models for stock return prediction in non-stationary environments, revealing a fundamental nonstationarity-complexity tradeoff: complex models reduce misspecification error but require longer training windows that introduce stronger non-stationarity. We resolve this tension with a novel model selection method that jointly optimizes model class and training window size using a tournament procedure that adaptively evaluates candidates on non-stationary validation data. Our theoretical analysis demonstrates that this approach balances misspecification error, estimation variance, and non-stationarity, performing close to the best model in hindsight. Applying our method to 17 industry portfolio returns, we consistently outperform standard rolling-window benchmarks, improving out-of-sample $R^2$ by 14-23% on average. During NBER-designated recessions, improvements are substantial: our method achieves positive $R^2$ during the Gulf War recession while benchmarks are negative, and improves $R^2$ in absolute terms by at least 80bps during the 2001 recession as well as superior performance during the 2008 Financial Crisis. Economically, a trading strategy based on our selected model generates 31% higher cumulative returns averaged across the industries.

Machine Learning (ML) has been a foundational topic in artificial intelligence (AI), providing both theoretical groundwork and practical tools for its exciting advancements. From ResNet for visual recognition to Transformer for vision-language alignment, the AI models have achieved superior capability to humans. Furthermore, the scaling law has enabled AI to initially develop general intelligence, as demonstrated by Large Language Models (LLMs). To this stage, AI has had an enormous influence on society and yet still keeps shaping the future for humanity. However, distribution shift remains a persistent ``Achilles' heel'', fundamentally limiting the reliability and general usefulness of ML systems. Moreover, generalization under distribution shift would also cause trust issues for AIs. Motivated by these challenges, my research focuses on \textit{Trustworthy Machine Learning under Distribution Shifts}, with the goal of expanding AI's robustness, versatility, as well as its responsibility and reliability. We carefully study the three common distribution shifts into: (1) Perturbation Shift, (2) Domain Shift, and (3) Modality Shift. For all scenarios, we also rigorously investigate trustworthiness via three aspects: (1) Robustness, (2) Explainability, and (3) Adaptability. Based on these dimensions, we propose effective solutions and fundamental insights, meanwhile aiming to enhance the critical ML problems, such as efficiency, adaptability, and safety.

Accurate spatial interpolation of the air quality index (AQI), computed from concentrations of multiple air pollutants, is essential for regulatory decision-making, yet AQI fields are inherently non-Gaussian and often exhibit complex nonlinear spatial structure. Classical spatial prediction methods such as kriging are linear and rely on Gaussian assumptions, which limits their ability to capture these features and to provide reliable predictive distributions. In this study, we propose \textit{deep classifier kriging} (DCK), a flexible, distribution-free deep learning framework for estimating full predictive distribution functions for univariate and bivariate spatial processes, together with a \textit{data fusion} mechanism that enables modeling of non-collocated bivariate processes and integration of heterogeneous air pollution data sources. Through extensive simulation experiments, we show that DCK consistently outperforms conventional approaches in predictive accuracy and uncertainty quantification. We further apply DCK to probabilistic spatial prediction of AQI by fusing sparse but high-quality station observations with spatially continuous yet biased auxiliary model outputs, yielding spatially resolved predictive distributions that support downstream tasks such as exceedance and extreme-event probability estimation for regulatory risk assessment and policy formulation.

Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to answer causal questions. In this paper, we want to make it clear that you \emph{can} answer any causal inference question within the realm of probabilistic modelling and inference, without causal-specific tools or notation. Through concrete examples, we demonstrate how causal questions can be tackled by writing down the probability of everything. Lastly, we reinterpret causal tools as emerging from standard probabilistic modelling and inference, elucidating their necessity and utility.