Deep neural networks achieve state-of-the-art performance in estimating heterogeneous treatment effects, but their opacity limits trust and adoption in sensitive domains such as medicine, economics, and public policy. Building on well-established and high-performing causal neural architectures, we propose causalKANs, a framework that transforms neural estimators of conditional average treatment effects (CATEs) into Kolmogorov--Arnold Networks (KANs). By incorporating pruning and symbolic simplification, causalKANs yields interpretable closed-form formulas while preserving predictive accuracy. Experiments on benchmark datasets demonstrate that causalKANs perform on par with neural baselines in CATE error metrics, and that even simple KAN variants achieve competitive performance, offering a favorable accuracy--interpretability trade-off. By combining reliability with analytic accessibility, causalKANs provide auditable estimators supported by closed-form expressions and interpretable plots, enabling trustworthy individualized decision-making in high-stakes settings. We release the code for reproducibility at https://github.com/aalmodovares/causalkans .

Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures targeting the same type of uncertainty (e.g., ensemble-based and density-based measures of epistemic uncertainty) may capture different failure modes. We take a multidimensional view on UQ by stacking complementary UQ measures into a vector. Such vectors are assigned with Monge-Kantorovich ranks produced by an optimal-transport-based ordering method. The prediction is then deemed more uncertain than the other if it has a higher rank. The resulting VecUQ-OT algorithm uses entropy-regularized optimal transport. The transport map is learned on vectors of scores from in-distribution data and, by design, applies to unseen inputs, including out-of-distribution cases, without retraining. Our framework supports flexible non-additive uncertainty fusion (including aleatoric and epistemic components). It yields a robust ordering for downstream tasks such as selective prediction, misclassification detection, out-of-distribution detection, and selective generation. Across synthetic, image, and text data, VecUQ-OT shows high efficiency even when individual measures fail. The code for the method is available at: https://github.com/stat-ml/multidimensional_uncertainty.

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated hyperparameter. The method estimates the hyperparameters by marginalizing out the weights and performing (marginalized) maximum likelihood (ML) estimation. SBL returns many hyperparameter estimates to diverge to infinity, effectively setting the estimates of the corresponding weights to zero (i.e., pruning the corresponding weights from the model) and thereby yielding a sparse estimate of the weight vector. In this letter, we analyze the marginal likelihood as function of a single hyperparameter while keeping the others fixed, when the Gaussian assumptions on the noise samples and the weight distribution that underlies the derivation of SBL are weakened. We derive sufficient conditions that lead, on the one hand, to finite hyperparameter estimates and, on the other, to infinite ones. Finally, we show that in the Gaussian case, the two conditions are complementary and coincide with the pruning condition of fast SBL (F-SBL), thereby providing additional insights into this algorithm.

Learning, whether natural or artificial, is a process of selection. It starts with a set of candidate options and selects the more successful ones. In the case of machine learning the selection is done based on empirical estimates of prediction accuracy of candidate prediction rules on some data. Due to randomness of data sampling the empirical estimates are inherently noisy, leading to selection under uncertainty. The book provides statistical tools to obtain theoretical guarantees on the outcome of selection under uncertainty. We start with concentration of measure inequalities, which are the main statistical instrument for controlling how much an empirical estimate of expectation of a function deviates from the true expectation. The book covers a broad range of inequalities, including Markov's, Chebyshev's, Hoeffding's, Bernstein's, Empirical Bernstein's, Unexpected Bernstein's, kl, and split-kl. We then study the classical (offline) supervised learning and provide a range of tools for deriving generalization bounds, including Occam's razor, Vapnik-Chervonenkis analysis, and PAC-Bayesian analysis. The latter is further applied to derive generalization guarantees for weighted majority votes. After covering the offline setting, we turn our attention to online learning. We present the space of online learning problems characterized by environmental feedback, environmental resistance, and structural complexity. A common performance measure in online learning is regret, which compares performance of an algorithm to performance of the best prediction rule in hindsight, out of a restricted set of prediction rules. We present tools for deriving regret bounds in stochastic and adversarial environments, and under full information and bandit feedback.

Abstract--Future networks are envisioned to connect massive artificial intelligence (AI) agents, enabling their extensive collaboration on diverse tasks. Compared to traditional entities, these agents naturally suit the semantic communication (SC), which can significantly enhance the bandwidth efficiency. Nevertheless, SC requires the knowledge among agents to be aligned, while agents have distinct expert knowledge for their individual tasks in practice. In this paper, we propose a distillation-enabled knowledge alignment protocol (DeKAP), which distills the expert knowledge of each agent into parameter-efficient low-rank matrices, allocates them across the network, and allows agents to simultaneously maintain aligned knowledge for multiple tasks. We formulate the joint minimization of alignment loss, communication overhead, and storage cost as a large-scale integer linear programming problem and develop a highly efficient greedy algorithm. From computer simulation, the DeKAP establishes knowledge alignment with the lowest communication and computation resources compared to conventional approaches. Future communication networks will usher in a new era of the "Internet of Intelligence," where human beings, devices, and a wide range of artificial intelligence (AI) agents are seamlessly interconnected [1].

The decline in interest rates and economic stabilization has heightened the importance of accurate mortality rate forecasting, particularly in insurance and pension markets. Multi-step-ahead predictions are crucial for public health, demographic planning, and insurance risk assessments; however, they face challenges when data are limited. Hybrid systems that combine statistical and Machine Learning (ML) models offer a promising solution for handling both linear and nonlinear patterns. This study evaluated the impact of different multi-step forecasting approaches (Recursive, Direct, and Multi-Input Multi-Output) and ML models on the accuracy of hybrid systems. Results from 12 datasets and 21 models show that the selection of both the multi-step approach and the ML model is essential for improving performance, with the ARIMA-LSTM hybrid using a recursive approach outperforming other models in most cases.

Can Ukraine restore its pre-war borders? Why are Tomahawk missiles for Ukraine a'red line' for Russia? Is Russia testing NATO with aerial incursions in Europe? Russian forces killed four people, including a 12-year-old girl, and injured 13 in an attack on Ukraine's capital, Kyiv, on Sunday night, Tymur Tkachenko, the head of Kyiv's military administration, wrote in a post on Telegram. Those killed also included staff and patients at a cardiology centre, Tkachenko added.

Denmark has barred civilian drones from its airspace before a European Union Summit, following reported sightings of drones at several military locations overnight on Saturday. The Nordic country has been on alert following a string of drone incidents over the past week, which have led to the closure of several airports. The ban will remain in place from Monday through Friday of the coming week, when Denmark, which holds the rotating presidency of the EU for the second half of this year, will be hosting European leaders. In a statement earlier in the day, the country's Ministry of Defence said it had "several capacities deployed" after the drone sighting, without elaborating on the deployment, the number of drones or the locations. The latest incident comes a day after the NATO military alliance announced it was upgrading its mission in the Baltic Sea with an air defence frigate in response to the drone incursion in Denmark. In a statement sent to the Reuters news agency, NATO said it would "conduct even more enhanced vigilance with new multi-domain assets in the Baltic Sea region".

Can Ukraine restore its pre-war borders? Why are Tomahawk missiles for Ukraine a'red line' for Russia? Is Russia testing NATO with aerial incursions in Europe? Heavy Russian drone attack kills at least four in Ukraine's capital Kyiv NewsFeed Heavy Russian drone attack kills at least four in Ukraine's capital Kyiv Russia has launched a heavy attack on Ukraine with hundreds of kamikaze drones hitting residential buildings in Kyiv. At least four people have been killed, including a 12-year-old girl.

'To them, ageing is a technical problem that can, and will, be fixed': how the rich and powerful plan to live for ever When Xi Jinping and Vladimir Putin were caught on mic talking about living for ever, it seemed straight out of a sci-fi fantasy. You have everything you could want at your disposal: power, influence, money. But, the problem is, your time at the top is fleeting. In early September, China's Xi Jinping and Russia's Vladimir Putin were caught on mic talking about strategies to stay young. "With the development of biotechnology, human organs can be continuously transplanted, and people can live younger and younger, and even achieve immortality," Putin said via an interpreter to Xi. "There's a chance," he continued, "of also living to 150 [years old]." But is this even possible, and what would it mean for the world if the people with power were able to live for ever? Over the centuries, we have used ever more sophisticated technology to heal ourselves into unprecedented longevity. In the 20th century, it was innovations in public health and medicine that effected this transformation, allowing today's children to live longer, healthier lives than at any time in history.