Understanding causality in event sequences with thousands of sparse event types is critical in domains such as healthcare, cybersecurity, or vehicle diagnostics, yet current methods fail to scale. We present OSCAR, a one-shot causal autoregressive method that infers per-sequence Markov Boundaries using two pretrained Transformers as density estimators. This enables efficient, parallel causal discovery without costly global CI testing. On a real-world automotive dataset with 29,100 events and 474 labels, OSCAR recovers interpretable causal structures in minutes, while classical methods fail to scale, enabling practical scientific diagnostics at production scale.

Dynamic Bayesian networks (DBNs) are compact graphical representations used to model probabilistic systems where interdependent random variables and their distributions evolve over time. In this paper, we study the verification of the evolution of conditional-independence (CI) propositions against temporal logic specifications. To this end, we consider two specification formalisms over CI propositions: linear temporal logic (LTL), and non-deterministic Büchi automata (NBAs). This problem has two variants. Stochastic CI properties take the given concrete probability distributions into account, while structural CI properties are viewed purely in terms of the graphical structure of the DBN. We show that deciding if a stochastic CI proposition eventually holds is at least as hard as the Skolem problem for linear recurrence sequences, a long-standing open problem in number theory. On the other hand, we show that verifying the evolution of structural CI propositions against LTL and NBA specifications is in PSPACE, and is NP- and coNP-hard. We also identify natural restrictions on the graphical structure of DBNs that make the verification of structural CI properties tractable.

Species distribution models (SDMs), which aim to predict species occurrence based on environmental variables, are widely used to monitor and respond to biodiversity change. Recent deep learning advances for SDMs have been shown to perform well on complex and heterogeneous datasets, but their effectiveness remains limited by spatial biases in the data. In this paper, we revisit deep SDMs from a Bayesian perspective and introduce BATIS, a novel and practical framework wherein prior predictions are updated iteratively using limited observational data. Models must appropriately capture both aleatoric and epistemic uncertainty to effectively combine fine-grained local insights with broader ecological patterns. We benchmark an extensive set of uncertainty quantification approaches on a novel dataset including citizen science observations from the eBird platform. Our empirical study shows how Bayesian deep learning approaches can greatly improve the reliability of SDMs in data-scarce locations, which can contribute to ecological understanding and conservation efforts.

Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural setting of star-structured variational inference, where a root variable impacts all the other ones. We prove the first results for existence, uniqueness, and self-consistency of the variational approximation. In turn, we derive quantitative approximation error bounds for the variational approximation to the posterior, extending prior work from the mean-field setting to the star-structured setting. We also develop a gradient-based algorithm with provable guarantees for computing the variational approximation using ideas from optimal transport theory. We explore the implications of our results for Gaussian measures and hierarchical Bayesian models, including generalized linear models with location family priors and spike-and-slab priors with one-dimensional debiasing. As a by-product of our analysis, we develop new stability results for star-separable transport maps which might be of independent interest.

The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a Bregman divergence, which is relevant to maximum likelihood estimation with exponential families. While the result is already known, there was not previously a clear, standalone derivation, so we provide one for pedagogical purposes. A version of this note previously appeared on the author's personal website without context. Here we provide additional discussion and references to the relevant prior literature.

Machine learning (ML) classification models are increasingly being used in a wide range of applications where it is important that predictions are accompanied by uncertainties, including in climate and earth observation, medical diagnosis and bioaerosol monitoring. The output of an ML classification model is a type of categorical variable known as a nominal property in the International Vocabulary of Metrology (VIM). However, concepts related to uncertainty evaluation for nominal properties are not defined in the VIM, nor is such evaluation addressed by the Guide to the Expression of Uncertainty in Measurement (GUM). In this paper we propose a metrological conceptual uncertainty evaluation framework for nominal properties. This framework is based on probability mass functions and summary statistics thereof, and it is applicable to ML classification. We also illustrate its use in the context of two applications that exemplify the issues and have significant societal impact, namely, climate and earth observation and medical diagnosis. Our framework would enable an extension of the GUM to uncertainty for nominal properties, which would make both applicable to ML classification models.

Motion prediction, recently popularized under the term world models, refers to anticipating the future states of agents or the future evolution of a scene, which is rooted in human cognition to bridge perception and decision-making, enabling us to anticipate, adapt, and act within an ever-changing world. It lies at the core of intelligent autonomous systems, such as robotics and self-driving cars, to safely operate in dynamic and human-robot-mixed environments, and also informs broader time-series challenges. With advances in methods, representations, and datasets, the field has seen rapid progress, reflected in rapidly updated benchmark performance. However, when state-of-the-art methods are deployed in the real world, they are often found to struggle to generalize to open-world settings and fall short of deployment standards. This reveals a gap between reality and benchmarks, which are often idealized or ill-posed, and fail to capture real-world complexity. To address the pressing need for problem settings that better reflect real-world challenges and guide future research, this paper focuses on revisiting the generalization and applicability of motion prediction models, with an emphasis on robotics, autonomous driving, and human motion applications. We first provide a comprehensive taxonomy of motion prediction methods, covering representations, modelling methods, application domains, and evaluation protocols. We then revisit two fundamental problems: 1) how to push motion prediction models to be deployable to realistic deployment standards, where motion prediction does not act in a vacuum, but functions as one module of closed-loop autonomy stacks - it takes input from the localization and perception, and informs downstream planning and control.

Context. As the number of detected transiting exoplanet candidates continues to grow, the need for robust and scalable automated tools to prioritize or validate them has become increasingly critical. Among the most promising solutions, deep learning models offer the ability to interpret complex diagnostic metrics traditionally used in the vetting process. Aims. In this work, we present WATSON-Net, a new open-source neural network classifier and data preparation package designed to compete with current state-of-the-art tools for vetting and validation of transiting exoplanet signals from space-based missions. Methods. Trained on Kepler Q1-Q17 DR25 data using 10-fold cross-validation, WATSON-Net produces ten independent models, each evaluated on dedicated validation and test sets. The ten models are calibrated and prepared to be extensible for TESS data by standardizing the input pipeline, allowing for performance assessment across different space missions. Results. For Kepler targets, WATSON-Net achieves a recall-at-precision of 0.99 (R@P0.99) of 0.903, ranking second, with only the ExoMiner network performing better (R@P0.99 = 0.936). For TESS signals, WATSON-Net emerges as the best-performing non-fine-tuned machine learning classifier, achieving a precision of 0.93 and a recall of 0.76 on a test set comprising confirmed planets and false positives. Both the model and its data preparation tools are publicly available in the dearwatson Python package, fully open-source and integrated into the vetting engine of the SHERLOCK pipeline.