Many modern data analysis problems involve inferences from streaming data.

Advanced TGNs utilize an RNN based memory module to represent a node's history as a

Musk becomes world's first half-trillionaire Tesla boss Elon Musk has become the first person ever to achieve a net worth of more than $500bn (£370.9bn), The tech magnate's net worth briefly reached $500.1bn on Wednesday afternoon New York time, before dipping slightly to just over $499bn later in the day, the Forbes billionaires index reported. Alongside Tesla, valuations of his other ventures, including the artificial intelligence start-up xAI and rocket company SpaceX, have also reportedly climbed in recent months. According to Forbes' billionaires index, Oracle founder Larry Ellison is the world's second richest person, with a fortune of about $350.7bn. Mr Ellison briefly overtook Musk last month after shares in Oracle soared by more than 40%, boosted by the firm's surprisingly rosy outlook for its cloud infrastructure business and artificial intelligence (AI) deals.

A data-driven approach, however, could overcome limitations in such rule-based approaches and improve precision mappings for individuals.

By making personalized suggestions, a recommender system is playing a crucial role in improving the engagement of users in modern web-services. However, most recommendation algorithms do not explicitly take into account the temporal behavior and the recurrent activities of users. Two central but less explored questions are how to recommend the most desirable item at the right moment, and how to predict the next returning time of a user to a service. To address these questions, we propose a novel framework which connects self-exciting point processes and low-rank models to capture the recurrent temporal patterns in a large collection of user-item consumption pairs. We show that the parameters of the model can be estimated via a convex optimization, and furthermore, we develop an efficient algorithm that maintains O (1 /null) convergence rate, scales up to problems with millions of user-item pairs and hundreds of millions of temporal events. Compared to other state-of-the-arts in both synthetic and real datasets, our model achieves superb predictive performance in the two time-sensitive recommendation tasks. Finally, we point out that our formulation can incorporate other extra context information of users, such as profile, textual and spatial features.

While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited. In this work, we establish the benefits of (generalized) weight normalization (WN) applied to the overparameterized matrix sensing problem. We prove that WN with Riemannian optimization achieves linear convergence, yielding an exponential speedup over standard methods that do not use WN. Our analysis further demonstrates that both iteration and sample complexity improve polynomially as the level of overparameterization increases. To the best of our knowledge, this work provides the first characterization of how WN leverages overparameterization for faster convergence in matrix sensing.

Wind farm placement arranges the size and the location of multiple wind farms within a given region. The power output is highly related to the wind speed on spatial and temporal levels, which can be modeled by advanced data-driven approaches. To this end, we use a probabilistic neural network as a surrogate that accounts for the spatiotemporal correlations of wind speed. This neural network uses ReLU activation functions so that it can be reformulated as mixed-integer linear set of constraints (constraint learning). We embed these constraints into the placement decision problem, formulated as a two-stage stochastic optimization problem. Specifically, conditional quantiles of the total electricity production are regarded as recursive decisions in the second stage. We use real high-resolution regional data from a northern region in Spain. We validate that the constraint learning approach outperforms the classical bilinear interpolation method. Numerical experiments are implemented on risk-averse investors. The results indicate that risk-averse investors concentrate on dominant sites with strong wind, while exhibiting spatial diversification and sensitive capacity spread in non-dominant sites. Furthermore, we show that if we introduce transmission line costs in the problem, risk-averse investors favor locations closer to the substations. On the contrary, risk-neutral investors are willing to move to further locations to achieve higher expected profits. Our results conclude that the proposed novel approach is able to tackle a portfolio of regional wind farm placements and further provide guidance for risk-averse investors.

Recovering a low-CP-rank tensor from noisy linear measurements is a central challenge in high-dimensional data analysis, with applications spanning tensor PCA, tensor regression, and beyond. We exploit the intrinsic geometry of rank-one tensors by casting the recovery task as an optimization problem over the Segre manifold, the smooth Riemannian manifold of rank-one tensors. This geometric viewpoint yields two powerful algorithms: Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN), each of which preserves feasibility at every iteration. Under mild noise assumptions, we prove that RGD converges at a local linear rate, while RGN exhibits an initial local quadratic convergence phase that transitions to a linear rate as the iterates approach the statistical noise floor. Extensive synthetic experiments validate these convergence guarantees and demonstrate the practical effectiveness of our methods.

Deep learning integration into medical imaging systems has transformed disease detection and diagnosis processes with a focus on pneumonia identification. The study introduces an intricate deep learning system using Convolutional Neural Networks for automated pneumonia detection from chest Xray images which boosts diagnostic precision and speed. The proposed CNN architecture integrates sophisticated methods including separable convolutions along with batch normalization and dropout regularization to enhance feature extraction while reducing overfitting. Through the application of data augmentation techniques and adaptive learning rate strategies the model underwent training on an extensive collection of chest Xray images to enhance its generalization capabilities. A convoluted array of evaluation metrics such as accuracy, precision, recall, and F1 score collectively verify the model exceptional performance by recording an accuracy rate of 91. This study tackles critical clinical implementation obstacles such as data privacy protection, model interpretability, and integration with current healthcare systems beyond just model performance. This approach introduces a critical advancement by integrating medical ontologies with semantic technology to improve diagnostic accuracy. The study enhances AI diagnostic reliability by integrating machine learning outputs with structured medical knowledge frameworks to boost interpretability. The findings demonstrate AI powered healthcare tools as a scalable efficient pneumonia detection solution. This study advances AI integration into clinical settings by developing more precise automated diagnostic methods that deliver consistent medical imaging results.