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.

Contextual predictability shapes both the form and choice of words in online language production. The effects of the predictability of a word given its previous context are generally well-understood in both production and comprehension, but studies of naturalistic production have also revealed a poorly-understood backward predictability effect of a word given its future context, which may be related to future planning. Here, in two studies of naturalistic speech corpora, we investigate backward predictability effects using improved measures and more powerful language models, introducing a new principled and conceptually motivated information-theoretic predictability measure that integrates predictability from both the future and the past context. Our first study revisits classic predictability effects on word duration. Our second study investigates substitution errors within a generative framework that independently models the effects of lexical, contextual, and communicative factors on word choice, while predicting the actual words that surface as speech errors. We find that our proposed conceptually-motivated alternative to backward predictability yields qualitatively similar effects across both studies. Through a fine-grained analysis of substitution errors, we further show that different kinds of errors are suggestive of how speakers prioritize form, meaning, and context-based information during lexical planning. Together, these findings illuminate the functional roles of past and future context in how speakers encode and choose words, offering a bridge between contextual predictability effects and the mechanisms of sentence planning.

Urban air pollution is a major health crisis causing millions of premature deaths annually, underscoring the urgent need for accurate and scalable monitoring of air quality (AQ). While low-cost sensors (LCS) offer a scalable alternative to expensive reference-grade stations, their readings are affected by drift, calibration errors, and environmental interference. To address these challenges, we introduce Veli (Reference-free Variational Estimation via Latent Inference), an unsupervised Bayesian model that leverages variational inference to correct LCS readings without requiring co-location with reference stations, eliminating a major deployment barrier. Specifically, Veli constructs a disentangled representation of the LCS readings, effectively separating the true pollutant reading from the sensor noise. To build our model and address the lack of standardized benchmarks in AQ monitoring, we also introduce the Air Quality Sensor Data Repository (AQ-SDR). AQ-SDR is the largest AQ sensor benchmark to date, with readings from 23,737 LCS and reference stations across multiple regions. Veli demonstrates strong generalization across both in-distribution and out-of-distribution settings, effectively handling sensor drift and erratic sensor behavior. Code for model and dataset will be made public when this paper is published.

Industrial smoke segmentation is critical for air-quality monitoring and environmental protection but is often hampered by the high cost and scarcity of pixel-level annotations in real-world settings. We introduce CEDANet, a human-in-the-loop, class-aware domain adaptation framework that uniquely integrates weak, citizen-provided video-level labels with adversarial feature alignment. Specifically, we refine pseudo-labels generated by a source-trained segmentation model using citizen votes, and employ class-specific domain discriminators to transfer rich source-domain representations to the industrial domain. Comprehensive experiments on SMOKE5K and custom IJmond datasets demonstrate that CEDANet achieves an F1-score of 0.414 and a smoke-class IoU of 0.261 with citizen feedback, vastly outperforming the baseline model, which scored 0.083 and 0.043 respectively. This represents a five-fold increase in F1-score and a six-fold increase in smoke-class IoU. Notably, CEDANet with citizen-constrained pseudo-labels achieves performance comparable to the same architecture trained on limited 100 fully annotated images with F1-score of 0.418 and IoU of 0.264, demonstrating its ability to reach small-sampled fully supervised-level accuracy without target-domain annotations. Our research validates the scalability and cost-efficiency of combining citizen science with weakly supervised domain adaptation, offering a practical solution for complex, data-scarce environmental monitoring applications.

The cost of error in many high-stakes settings is asymmetric: misdiagnosing pneumonia when absent is an inconvenience, but failing to detect it when present can be life-threatening. Because of this, artificial intelligence (AI) models used to assist such decisions are frequently trained with asymmetric loss functions that incorporate human decision-makers' trade-offs between false positives and false negatives. In two focal applications, we show that this standard alignment practice can backfire. In both cases, it would be better to train the machine learning model with a loss function that ignores the human's objective and then adjust predictions ex post according to that objective. We rationalize this result using an economic model of incentive design with endogenous information acquisition. The key insight from our theoretical framework is that machine classifiers perform not one but two incentivized tasks: choosing how to classify and learning how to classify. We show that while the adjustments engineers use correctly incentivize choosing, they can simultaneously reduce the incentives to learn. Our formal treatment of the problem reveals that methods embraced for their intuitive appeal can in fact misalign human and machine objectives in predictable ways.