Inference-time alignment for diffusion models aims to adapt a pre-trained diffusion model toward a target distribution without retraining the base score network, thereby preserving the generative capacity of the base model while enforcing desired properties at the inference time. A central mechanism for achieving such alignment is guidance, which modifies the sampling dynamics through an additional drift term. In this work, we introduce Doob's matching, a novel framework for guidance estimation grounded in Doob's $h$-transform. Our approach formulates guidance as the gradient of logarithm of an underlying Doob's $h$-function and employs gradient-penalized regression to simultaneously estimate both the $h$-function and its gradient, resulting in a consistent estimator of the guidance. Theoretically, we establish non-asymptotic convergence rates for the estimated guidance. Moreover, we analyze the resulting controllable diffusion processes and prove non-asymptotic convergence guarantees for the generated distributions in the 2-Wasserstein distance.

Driven by the right to be forgotten (RTBF), machine unlearning has become an essential requirement for privacy-preserving machine learning. However, its realization in decentralized federated learning (DFL) remains largely unexplored. In DFL, clients exchange local updates only with neighbors, causing model information to propagate and mix across the network. As a result, when a client requests data deletion, its influence is implicitly embedded throughout the system, making removal difficult without centralized coordination. We propose a novel certified unlearning framework for DFL based on Newton-style updates. Our approach first quantifies how a client's data influence propagates during training. Leveraging curvature information of the loss with respect to the target data, we then construct corrective updates using Newton-style approximations. To ensure scalability, we approximate second-order information via Fisher information matrices. The resulting updates are perturbed with calibrated noise and broadcast through the network to eliminate residual influence across clients. We theoretically prove that our approach satisfies the formal definition of certified unlearning, ensuring that the unlearned model is difficult to distinguish from a retrained model without the deleted data. We also establish utility bounds showing that the unlearned model remains close to retraining from scratch. Extensive experiments across diverse decentralized settings demonstrate the effectiveness and efficiency of our framework.

Foundation models pre-trained on large-scale source datasets are reshaping the traditional training paradigm for time series classification. However, existing time series foundation models primarily focus on forecasting tasks and often overlook classification-specific challenges, such as modeling interpretable shapelets that capture class-discriminative temporal features. To bridge this gap, we propose UniShape, a unified shape-aware foundation model designed for time series classification. UniShape incorporates a shape-aware adapter that adaptively aggregates multiscale discriminative subsequences (shapes) into class tokens, effectively selecting the most relevant subsequence scales to enhance model interpretability. Meanwhile, a prototype-based pretraining module is introduced to jointly learn instance- and shape-level representations, enabling the capture of transferable shape patterns. Pre-trained on a large-scale multi-domain time series dataset comprising 1.89 million samples, UniShape exhibits superior generalization across diverse target domains. Experiments on 128 UCR datasets and 30 additional time series datasets demonstrate that UniShape achieves state-of-the-art classification performance, with interpretability and ablation analyses further validating its effectiveness.

Community detection is a fundamental task in data analysis. Block models form a standard approach to partition nodes according to a graph model, facilitating the analysis and interpretation of the network structure. By grouping nodes with similar connection patterns, they enable the identification of a wide variety of underlying structures. The degree-corrected block model (DCBM) is an established model that accounts for the heterogeneity of node degrees. However, existing inference methods for the DCBM are heuristics that are highly sensitive to initialization, typically done randomly. In this work, we show that DCBM inference can be reformulated as a constrained nonnegative matrix factorization problem. Leveraging this insight, we propose a novel method for community detection and a theoretically well-grounded initialization strategy that provides an initial estimate of communities for inference algorithms. Our approach is agnostic to any specific network structure and applies to graphs with any structure representable by a DCBM, not only assortative ones. Experiments on synthetic and real benchmark networks show that our method detects communities comparable to those found by DCBM inference, while scaling linearly with the number of edges and communities; for instance, it processes a graph with 100,000 nodes and 2,000,000 edges in approximately 4 minutes. Moreover, the proposed initialization strategy significantly improves solution quality and reduces the number of iterations required by all tested inference algorithms. Overall, this work provides a scalable and robust framework for community detection and highlights the benefits of a matrix-factorization perspective for the DCBM.

Supporting Go/No-Go decisions prior to launch requires assessing real-time telemetry data against redline limits established during the design qualification phase. Family data from ground testing or previous flights is commonly used to detect initiating failure modes and their timing; however, this approach relies heavily on engineering judgment and is more error-prone for new launch vehicles. To address these limitations, we utilize Long-Term Short-Term Memory (LSTM) networks for supervised classification of time-series anomalies. Although, initial training labels derived from simulated anomaly data may be suboptimal due to variations in anomaly strength, anomaly settling times, and other factors. In this work, we propose a novel statistical detector based on the Mahalanobis distance and forward-backward detection fractions to adjust the supervised training labels. We demonstrate our method on digital twin simulations of a ground-stage propulsion system with 20.8 minutes of operation per trial and O(10^8) training timesteps. The statistical data relabeling improved precision and recall of the LSTM classifier by 7% and 22% respectively.

Meta-learning methods for regression like Neural (Diffusion) Processes achieve impressive results, but with these models it can be difficult to incorporate expert prior knowledge and information contained in metadata. Large Language Models (LLMs) are trained on giant corpora including varied real-world regression datasets alongside their descriptions and metadata, leading to impressive performance on a range of downstream tasks. Recent work has extended this to regression tasks and is able to leverage such prior knowledge and metadata, achieving surprisingly good performance, but this still rarely matches dedicated meta-learning methods. Here we introduce a general method for sampling from a product-of-experts of a diffusion or flow matching model and an `expert' with binned probability density; we apply this to combine neural diffusion processes with LLM token probabilities for regression (which may incorporate textual knowledge), exceeding the empirical performance of either alone.

Cardiovascular disease (CVD) continues to be the major cause of death globally, calling for predictive models that not only handle diverse and high-dimensional biomedical signals but also maintain interpretability and privacy. We create a single multimodal learning framework that integrates cross modal transformers with graph neural networks and causal representation learning to measure personalized CVD risk. The model combines genomic variation, cardiac MRI, ECG waveforms, wearable streams, and structured EHR data to predict risk while also implementing causal invariance constraints across different clinical subpopulations. To maintain transparency, we employ SHAP based feature attribution, counterfactual explanations and causal latent alignment for understandable risk factors. Besides, we position the design in a federated, privacy, preserving optimization protocol and establish rules for convergence, calibration and uncertainty quantification under distributional shift. Experimental studies based on large-scale biobank and multi institutional datasets reveal state discrimination and robustness, exhibiting fair performance across demographic strata and clinically distinct cohorts. This study paves the way for a principled approach to clinically trustworthy, interpretable and privacy respecting CVD prediction at the population level.

Calibration Bands for Mean Estimates within the Exponential Dispersion Family null Lukasz Delong Selim Gatti Mario V. W uthrich Version of October 8, 2025 Abstract A statistical model is said to be calibrated if the resulting mean estimates perfectly match the true means of the underlying responses. Aiming for calibration is often not achievable in practice as one has to deal with finite samples of noisy observations. A weaker notion of calibration is auto-calibration. An auto-calibrated model satisfies that the expected value of the responses for a given mean estimate matches this estimate. Testing for auto-calibration has only been considered recently in the literature and we propose a new approach based on calibration bands. Calibration bands denote a set of lower and upper bounds such that the probability that the true means lie simultaneously inside those bounds exceeds some given confidence level. Such bands were constructed by Yang-Barber (2019) for sub-Gaussian distributions. Dimitriadis et al. (2023) then introduced narrower bands for the Bernoulli distribution. We use the same idea in order to extend the construction to the entire exponential dispersion family that contains for example the binomial, Poisson, negative binomial, gamma and normal distributions. Moreover, we show that the obtained calibration bands allow us to construct various tests for calibration and auto-calibration, respectively. As the construction of the bands does not rely on asymptotic results, we emphasize that our tests can be used for any sample size. Auto-calibration, calibration, calibration bands, exponential dispersion family, mean estimation, regression modeling, binomial distribution, Poisson distribution, negative binomial distribution, gamma distribution, normal distribution inverse Gaussian distribution. 1 Introduction Various statistical methods can be used to derive mean estimates from available observations, and it is important to understand whether these mean estimates are reliable for decision making. A statistical model is said to be calibrated if the resulting mean estimates perfectly match the true means of the underlying responses. In practice, calibration is often not achievable, as estimates are obtained from finite samples of noisy observations.

U.K.'s Starmer escalates threats against X, calls Grok'shameful' U.K.'s prime minister escalated threats against Elon Musk's X, vowing to enforce a law that bans the sexualization of people's images without consent and calling such content generated by Grok disgusting and shameful. U.K. Prime Minister Keir Starmer escalated his threats against Elon Musk's X on Monday, vowing to enforce a law that banned the sexualization of people's images without their consent and calling such content generated by Grok "disgusting and shameful." From this week, the government will enforce the offense established in last year's Data Act, which made the creation of nonconsensual intimate images illegal. Starmer told members of Parliament on Monday, "if X cannot control Grok, we will -- and we'll do it fast because if you profit from harm and abuse, you lose the right to self regulate." Starmer accused X of protecting "abusive users" instead of the women and children whose images have been exploited, describing it as a "total distortion of priorities."

The UK government is threatening to ban Elon Musk's X platform after Technology Secretary Liz Kendall confirmed an investigation into AI-generated sexual abuse images.