We study high-dimensional LASSO under differential privacy via objective perturbation with heterogeneous covariate scales. In practical scenarios, covariates often exhibit diverse scales; however, standard preprocessing is problematic under privacy constraints, as it consumes additional privacy budget. This heterogeneity induces effective anisotropy in the objective perturbation via the inverse Gram matrix of covariates, which can degrade the stability and accuracy of algorithms. To address this, we propose a Gram-based anisotropic objective perturbation, a ``pre-distortion" strategy that counteracts the distortion from the covariate structure to restore isotropy in the estimation process. Using an Approximate Message Passing (AMP) framework and state evolution analysis, we demonstrate that our proposed perturbation significantly stabilizes convergence and improves both statistical efficiency and privacy performance compared to standard uniform noise injection. Our results provide theoretical insights into designing stable and efficient private estimators without relying on data-dependent preprocessing.

In 2011, Judea Pearl received the Turing Award, considered the Nobel Prize in Computing, for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning. It includes pioneering the development of causal discovery algorithms. These computer algorithms can analyze large multivariate datasets and automatically discover the causal relationships among the constituent variables. They have been widely used in many critical fields such as medicine and economics to support decisions. However, to our knowledge, they have not been leveraged in law. This paper attempts to alleviate this gap by investigating whether causal discovery algorithms can be leveraged for automated generation of legal arguments. To that end, a novel legal dataset is prepared by identifying 17 legal concepts, such as physical assault and property dispute. A curated collection of 150 homicide cases are annotated with these concepts, e.g., a case is annotated with physical assault only if a physical assault had been reported in that case. Subsequently, a selected set of widely-used causal discovery algorithms is applied to the annotated dataset to discover the causal relationships between the legal concepts. Additionally, the degrees of belief associated with the discovered relationships are quantified in mathematical probabilities. It is shown that some of the causal relationships help generate viable legal arguments, e.g., if one could establish that a physical assault has not taken place during a homicide, it should be a sufficient condition (with probability 1) to establish that the homicide has not been committed due to a property-related dispute. Thus, this paper shows that causal discovery algorithms can be helpful in generating legal arguments, opening up avenues for promising future endeavors.

The proliferation of large-scale and structurally complex data has spurred the integration of machine learning methods into statistical modeling. Recurrent neural networks (RNNs), a foundational class of models for time-dependent data, can be viewed as nonlinear extensions of classical autoregressive moving average models. Despite their flexibility and empirical success in machine learning, RNNs often suffer from limited interpretability and slow training, which hinders their use in statistics. This paper proposes the Parallelized RNN (ParaRNN), a novel model composed of multiple small recurrent units. ParaRNN admits an additive representation that decouples recurrent dynamics into interpretable components, whose behavior can be characterized through recurrence features. This interpretability enables its applications in nonparametric regression for time-dependent data, while the design also allows efficient parallelization. The approximation capacity and non-asymptotic prediction error bounds in a nonparametric regression setting are established for ParaRNN. Empirical results on three sequential modeling tasks further demonstrate that ParaRNN achieves performance comparable to vanilla RNNs while offering improved interpretability and efficiency.

A text scam impersonating state courts demands drivers pay $6.99 for fake traffic violations via QR codes. The scheme has hit residents in at least eight U.S. states.

Met Gala rocked as staff make revolting discovery hidden inside museum just hours before fashion's biggest night Shark Tank star Lori Greiner issues warning to 1.8bn Gmail users over hidden email setting I took an identical grocery list to Costco, Walmart and Target. The price difference for everyday items will shock you... but here's why I don't think the cheapest store is worth it Kobe Bryant's widow Vanessa speaks out on pregnancy and remarriage rumors six years on from Lakers legend's death America's fashion queen revealed as DailyMail+ unveils the Power List that humiliates Hollywood royalty, stuns Washington's elite... and leaves Lauren Sanchez reeling Britney Spears pleads guilty in DUI case and is sentenced to 12 months' probation as lawyer appears in court on her behalf Buc-ee's makes major rule change that leaves gas station fans furious My husband built a $250m empire but made me feel worthless. Our marriage was all but over... but my selfish act has deepened our intimacy in unimaginable ways Bianca Censori goes completely nude under sheer catsuit to visit med spa and leaves with noticeably fuller lips... while Kanye West waits in the car Trump threatens Iran will be'blown off the face of the earth' as missiles and drones target US ships.... and hits critical allies Warning as deadly venomous insect imported from China invades 20 US states... is your hometown at risk? Unsavory behaviors that risk toppling socialites from the front row... and how others stay on top Loyal McDonald's customer sipping his daily sweet tea spits drink out after feeling something SQUIRM through his straw US Open golf chief gives update on Tiger Woods' participation in the wake of DUI crash, arrest and rehab stint Innocent teen plunged into'sugar daddy' nightmare after posting video of her high school graduation ceremony online Shark Tank star Lori Greiner issues warning to 1.8bn Gmail users over hidden email setting A Shark Tank star has issued a stark safety warning to Gmail users about a default setting enabling Google to scan'every single' email. Lori Greiner, famous for her investments in products like Scrub Daddy and Squatty Potty, posted a video on her Instagram, urging users to block Google's AI in their accounts. 'Google doesn't want you to know this, but they've been allowing AI to scan every single one of your emails,' she said, adding that it includes'financial documents, tax information and personal conversations.'

The United Arab Emirates has said its air defences are engaging with missile attacks and incoming drones from Iran. The UAE Ministry of Defense said late on Monday afternoon that it was intercepting ballistic missiles, cruise missiles, and drones across the country. The emirate of Fujairah said that an Iranian drone sparked a fire at an oil facility. Civil defence teams were deployed immediately to contain the blaze, the Fujairah Media office said in a statement. There were no immediate reports of casualties.

Meta Platforms' roughly $2 billion acquisition of AI startup Manus was blocked by China's regulators, who required all parties to withdraw from the deal.

How well do you know Iran? What is the Ukrainian anti-drone system Sky Map being used in the Gulf? Cheap, mass-produced one-way drones have played a major role in the conflict between the United States, Israel and Iran since the first attacks on Tehran on February 28. As Iran uses these drones to target energy facilities, airbases and other strategic sites across the Gulf and Israel, the US and Israel use expensive interceptor missiles for defence. To counter the drone threat, Gulf states and their US partners have turned to Ukrainian-made anti-drone technology, battle-tested against Russian drone attacks.

A Ukrainian drone hit an upmarket residential high-rise in Moscow in the early hours of Monday, resulting in no casualties but causing visible damage to the façade of the building. It was the third night in a row that the Russian capital came under attack from drones, days before Russia holds a scaled-back 9 May parade to mark the Soviet Union's victory over Nazi Germany. An unverified video circulating on social media showed firemen entering a heavily damaged flat covered in dust and rubble and with blown-out windows, while another showed drone debris strewn across the street below. Two other drones were intercepted, Mayor Sergei Sobyanin said. Vnukovo and Domodedovo international airports suspended operations overnight.

Dating Is a Rich Person's Game Now People actually can't afford to date anymore. Ask just about anyone what's wrong with modern dating and they will likely tell you the same thing: The apps suck. They're built on a pay-to-win model. Fewer people are finding quality partners. Some studies have even suggested that increased time on them leads to higher depression and anxiety while also contributing to loneliness among men .