Why is Israel still in southern Lebanon? A war to shape Lebanon's future Was Israeli PM's Lebanon destruction video a snub to Trump? NewsFeed Was Israeli PM's Lebanon destruction video a snub to Trump? Hours after US President Donald Trump asked Benjamin Netanyahu to stop destroying buildings in Lebanon as it "makes Israel look bad", the Israeli prime minister published a montage of forces blowing up infrastructure across southern Lebanon.

Two full moons in one month occurs about once every 2.5 years. 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. The Eta Aquariids meteor shower appears in the night sky in Kandalama, Sri Lanka, on May 5, 2024. Unlike most major annual meteor showers, there is no sharp peak for this shower, but rather a broad maximum with good rates that last approximately one week. Breakthroughs, discoveries, and DIY tips sent six days a week.

Plus: Google, Microsoft, Amazon and Meta have all set AI spending records. In the past, getting to the North Pole involved a treacherous trip through ice many meters thick. But last year, a research vessel encountered open water and thin ice, which created an easy passage. It provided a reminder of how quickly the Arctic is changing. Now scientists are digging deep below the seabed to find out if the Arctic Ocean was ever ice-free--and what that could mean for the future of Earth's northernmost waters. Here's what they hope to discover .

Japan Airlines says it will trial humanoid robots as workers at Tokyo's Haneda Airport, with tasks including baggage handling and cabin cleaning.

Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models considering composite hypotheses tests. We derive a mathematical framework to study standard meta-analysis testing approaches in the context of the many normal means model, which serves as the platform to investigate more complex models. We introduce a natural and mild restriction on the meta-level combination functions of the local trials. This allows us to mathematically quantify the cost of compressing m trials into real-valued test statistics and combining these. We then derive minimax lower and matching upper bounds for the separation rates of standard combination methods for e.g.

Representation learning based on multi-task pretraining has become a powerful approach in many domains. In particular, task-aware representation learning aims to learn an optimal representation for a specific target task by sampling data from a set of source tasks, while task-agnostic representation learning seeks to learn a universal representation for a class of tasks. In this paper, we propose a general and versatile algorithmic and theoretic framework for active representation learning, where the learner optimally chooses which source tasks to sample from. This framework, along with a tractable meta algorithm, allows most arbitrary target and source task spaces (from discrete to continuous), covers both task-aware and task-agnostic settings, and is compatible with deep representation learning practices. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. In the bilinear case, by leveraging the non-uniform spectrum of the task representation and the calibrated source-target relevance, we prove that the sample complexity to achieve ε-excess risk on target scales with (k)2 v 22ε 2 where k is the effective dimension of the target and v 22 (0,1] represents the connection between source and target space. Compared to the passive one, this can save up to 1dW of sample complexity, where dW is the task space dimension. Finally, we demonstrate different instantiations of our meta algorithm in synthetic datasets and robotics problems, from pendulum simulations to real-world drone flight datasets. On average, our algorithms outperform baselines by 20% 70%. 1

Fréchet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and noiseless covariate data. In this paper, we present a novel estimation method that tackles these limitations by leveraging the low-rank structure inherent in the covariate matrix. Our proposed framework combines the concepts of global Fréchet regression and principal component regression, aiming to improve the efficiency and accuracy of the regression estimator. By incorporating the low-rank structure, our method enables more effective modeling and estimation, particularly in high-dimensional and errors-in-variables regression settings. We provide a theoretical analysis of the proposed estimator's large-sample properties, including a comprehensive rate analysis of bias, variance, and additional variations due to measurement errors. Furthermore, our numerical experiments provide empirical evidence that supports the theoretical findings, demonstrating the superior performance of our approach. Overall, this work introduces a promising framework for regression analysis of non-Euclidean variables, effectively addressing the challenges associated with limited and noisy covariate data, with potential applications in diverse fields.