Missing data is a common problem across various scientific disciplines, including medical research (Bell et al., 2014), social sciences (Molenberghs et al., 2014), and astronomy (Ivezi c et al., 2020). To handle missing entries in the dataset, imputation (Grzesiak et al., 2025; Kim and Shao, 2021; Little and Rubin, 2019) is a popular approach that is widely accepted in practice. An imputation model generates plausible values for each missing entry, transforming an incomplete dataset into a complete one. The critical importance of this task has led to the development of a wide array of imputation models, grounded in various modeling assumptions. These range from traditional approaches like hot-deck imputation (Little and Rubin, 2019) to more sophisticated methods such as Multiple Imputation via Chained Equations (MICE; V an Buuren and Groothuis-Oudshoorn 2011), random forest imputation (Stekhoven and Bühlmann, 2012), techniques based on Markov assumptions on graphs (Y ang and Chen, 2025), and even generative adversarial networks (Y oon et al., 2018). Despite the proliferation of imputation models, the selection of an optimal imputation model for a given dataset remains a significant challenge, largely due to the unsupervised nature of the problem. Among the many proposed strategies for evaluating and selecting imputation models, masking has emerged as a particularly popular procedure (Gelman et al., 1998; Honaker et al., 2011; Leek et al., 2012; Qian et al., 2024; Troyanskaya et al., 2001; Wang et al., 2024). Masking involves intentionally creating missing values in observed entries to create a setting where imputation accuracy can be measured against a known ground truth. This approach has demonstrated remarkable success and power in other domains, notably in language modeling (Devlin et al., 2019; Y ang et al., 2019) and image recognition (Hondru et al., 2025; Vincent et al., 2010; Xie et al., 2022) and prediction-powered inference (Angelopoulos et al., 2023; Wang et al., 2020).

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.

Establishing a communication system is hard because the intended meaning of a signal is unknown to its receiver when first produced, and the signaller also has no idea how that signal will be interpreted. Most theoretical accounts of the emergence of communication systems rely on feedback to reinforce behaviours that have led to successful communication in the past. However, providing such feedback requires already being able to communicate the meaning that was intended or interpreted. Therefore these accounts cannot explain how communication can be bootstrapped from non-communicative behaviours. Here we present a model that shows how a communication system, capable of expressing an unbounded number of meanings, can emerge as a result of individual behavioural differences in a large population without any pre-existing means to determine communicative success. The two key cognitive capabilities responsible for this outcome are behaving predictably in a given situation, and an alignment of psychological states ahead of signal production that derives from shared intentionality. Since both capabilities can exist independently of communication, our results are compatible with theories in which large flexible socially-learned communication systems like language are the product of a general but well-developed capacity for social cognition.

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.

Rectified Flow (RF) has been widely used as an effective generative model. Although RF is primarily based on probability flow Ordinary Differential Equations (ODE), recent studies have shown that injecting noise through reverse-time Stochastic Differential Equations (SDE) for sampling can achieve superior generative performance. Inspired by Positive-incentive Noise (pi-noise), we propose an innovative generative algorithm to train pi-noise generators, namely Rectified Noise (RN), which improves the generative performance by injecting pi-noise into the velocity field of pre-trained RF models. After introducing the Rectified Noise pipeline, pre-trained RF models can be efficiently transformed into pi-noise generators. We validate Rectified Noise by conducting extensive experiments across various model architectures on different datasets. Notably, we find that: (1) RF models using Rectified Noise reduce FID from 10.16 to 9.05 on ImageNet-1k. (2) The models of pi-noise generators achieve improved performance with only 0.39% additional training parameters.

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.

Abstract-- We challenge the long-standing assumption that exhaustive scene modeling is required for high-performance end-to-end autonomous driving (E2EAD). Inspired by cognitive science, we propose that effective planning arises not from reconstructing the world, but from the co-evolution of belief and intent within a minimal set of semantically rich tokens. Experiments on the nuPlan benchmark (720 scenarios, 11k+ samples) reveal three principles: (1) sparse intent tokens alone achieve 0.487 m ADE, demonstrating strong performance without future prediction; (2) conditioning trajectory decoding on predicted future tokens reduces ADE to 0.382 m, a 21.6% improvement, showing that performance emerges from cognitive planning; and (3) explicit reconstruction loss degrades performance, confirming that task-driven belief-intent co-evolution suffices under reliable perception inputs. Crucially, we observe the emergence of cognitive consistency: through prolonged training, the model spontaneously develops stable token dynamics that balance current perception (belief) and future goals (intent). This process, accompanied by "temporal fuzziness," enables robustness under uncertainty and continuous self-optimization. Our work establishes a new paradigm: intelligence lies not in pixel fidelity, but in the tokenized duality of belief and intent. Note: Numerical comparisons with methods reporting results on nuScenes are indicative only, as nuPlan presents a more challenging planning-focused evaluation.