Learning effective policies for adaptive data acquisition remains challenging: posterior-based methods rely on surrogate models and posterior approximations that can be misspecified or biased, while direct policy-learning methods map from historical observations and fail to exploit available model representations, making learning harder. We introduce policy learning with belief representations (POLAR), based on the insight that optimal data acquisition depends on the observation history only through a sufficient belief state. Specifically, POLAR decouples representation learning from policy learning by leveraging pretrained predictive foundation models as belief-state encoders, training a policy head on top of their representations. This yields a simple, unified amortised policy learning framework for Bayesian experimental design, Bayesian optimisation, and active learning, differing only in the task-specific utility used to train the policy. Empirically, we find that POLAR outperforms state-of-the-art amortised methods across diverse tasks while requiring far fewer training samples, demonstrating a significant step in the scalability and efficiency of amortised data acquisition.

Synthetic data augmentation is widely used to mitigate class imbalance, but its theoretical effects on score-based classification remain poorly understood. This paper develops a framework for characterizing when synthetic minority augmentation can improve threshold-integrated and threshold-optimized metrics, including AUROC, AUPRC, best-threshold balanced accuracy, and best-threshold \(\F_1\) score. We separate the effect of augmentation into two components: a change in effective class weighting and a discrepancy between the synthetic and true minority distributions. Under well-specified score models, the raw estimator already targets the likelihood-ratio ordering, which is population-optimal for the metrics considered. Consequently, augmentation cannot provide a fundamental population-level improvement beyond possible finite-sample variance reduction, and may introduce additional bias through synthetic distributional error. We further establish minimax lower bounds showing that the raw estimator already achieves the optimal metric-regret rate in the well-specified regime. Under misspecification, however, augmentation can play a qualitatively different role: by changing the effective class balance, it can alter the restricted-class projection and correct ranking errors induced by the raw imbalanced objective. We provide explicit improvement bounds quantifying the roles of approximation error, finite-sample estimation error, and synthetic distributional error. Simulation studies corroborate the theory, demonstrating limited gains under well-specification and nontrivial but nonmonotone improvements under misspecification.

State-space models provide a powerful framework for describing the evolution of hidden states in dynamical systems [3], [4], [1]. Conventionally, state-space models assume Gaussian measurement and state noise, owing to their tractability and well-characterized statistical properties. However, many real-world phenomena are subject to perturbations that deviate from the conventional Gaussian noise assumption. In radio interferometry, for instance, observational data are frequently corrupted by non-Gaussian noise sources such as radio-frequency interference (RFI) [5], [2], which originates from man-made signals and introduces significant distortions into astronomical measurements [6], [30]. Such interference produces sporadic high-power spikes in the measured visibilities, leading to heavy-tailed statistics. Many radio-interferometric reconstruction methods assume Gaussian additive noise [7], [31], [33], [35], an approximation that can lead to inaccurate reconstructions when the heavy-tailed nature of real-world measurement noise is not properly accounted for. In the realm of state-space modeling, addressing non-Gaussian noise has led to the development of various methodological approaches, notably particle filtering and non-conventional Kalman filters. Particle filters [8], or Sequential Monte Carlo methods, are designed to handle non-linear and non-Gaussian state-space models by representing the posterior distribution with a set of weighted samples [9], [10], [32].

Survival analysis is central to clinical decision-making, yet reliable time-to-event models require large, diverse cohorts that are rarely available at a single institution, while privacy regulations restrict the centralization of patient data. Federated learning (FL) offers a privacy-preserving alternative by training shared models without exchanging raw data, but its effectiveness for survival modeling under realistic, heterogeneous conditions remains insufficiently understood. This paper presents a systematic, multi-model evaluation of federated survival analysis on a cross-institutional breast cancer cohort with naturally heterogeneous distributed clients. Three representative survival models, the Cox Proportional Hazards model, DeepSurv, and Random Survival Forest (RSF), are compared across centralized, local, and federated training, and three federated optimization strategies (FedAvg, FedProx, and FedAdam) are assessed for the gradient-based models. Results show that FL consistently outperforms local training and approaches, and occasionally exceeds, centralized performance, while RSF offers the best overall balance of discrimination, calibration, and robustness across heterogeneous clients. We further find that performance depends on the diversity of client distributions, and that FedAvg and FedProx are stronger and more stable than FedAdam. Based on these findings, we derive practical, decision-oriented guidelines mapping data, privacy, interpretability, and resource constraints to recommended model and training-paradigm choices for federated survival modeling in healthcare.

Causal discovery seeks to uncover the causal dependencies among variables. For this purpose, we propose an algorithm called Tensor-based Second-order Causal Discovery (TSCD). Its input is a tensor obtained from the covariance matrices of observational and interventional data. Assuming the causal dependencies follow a linear structural equation model on a directed acyclic graph (DAG), TSCD outputs the DAG and the functions on its edges, requiring only that the noise variables are uncorrelated. We also implement a version of the approach for nonlinear models. Our focus on second-order statistics (via the covariance matrices) is motivated by their statistical and computational efficiency relative to higher-order moments, their identifiability relative to first-order statistics, and that they work regardless of whether the variables are Gaussian. We show that TSCD has identifiable causal order and parameters from a number of interventions that is logarithmic in the number of variables. Experiments show that TSCD is robust to noise, competitive with existing methods, and scales to hundreds of variables.

The growing reliance on machine learning for decisions across sectors underscores the importance of model transparency and interpretability. Existing post-hoc explainability methods and inherently interpretable approaches shed light on model behavior, yet they primarily reveal how models exploit correlations to maximize performance in prediction tasks. However, many decisions require causal insights and the possibility of using models for what-if scenario evaluation. To address this, we propose the integration of causal machine learning with inherently interpretable models for cross-sectional data. We evaluate these methods in terms of predictive accuracy and interpretability. Our findings show that the proposed approach achieves competitive performance in prediction and what-if analysis while offering transparency on the system structure, causal relationships among variables, and the functional forms that connect them. This work contributes to research on causality, machine learning interpretability, and data-driven decision support by offering informed, transparent, and causally grounded decisions.

Attention mechanisms have demonstrated remarkable empirical success in identifying relevant information from large collections of tokens, yet the theoretical principles underlying this behavior remain poorly understood. We study a stylized softmax-attention model in which a query vector is learned by stochastic gradient ascent from a collection of informative and nuisance tokens. Exploiting the symmetry of the model, we derive a population objective and characterize the limiting ordinary differential equation governing the learning dynamics. Using tools from stochastic approximation and dynamical systems theory, we establish a rigorous connection between the stochastic learning algorithm and its deterministic limit. Our main result shows that, under suitable high-dimensional scaling assumptions and standard step-size conditions, the learned query converges almost surely to the one-dimensional signal subspace spanned by the latent informative direction. Equivalently, the query asymptotically recovers the latent signal up to the intrinsic sign ambiguity. These results provide a rigorous theoretical foundation for understanding attention mechanisms as signal extraction procedures in high-dimensional noisy environments and offer a dynamical-systems perspective on how attention discovers relevant information in the presence of substantial noise.

Visual assessment of residual plots is a common approach for diagnosing linear models, but it relies on manual evaluation, which does not scale well and can lead to inconsistent decisions across analysts. The lineup protocol, which embeds the observed plot among null plots, can reduce subjectivity but requires even more human effort. In today's data-driven world, such tasks are well suited for automation. We present a new R package that uses a computer vision model to automate the evaluation of residual plots. An accompanying Shiny application is provided for ease of use. Given a sample of residuals, the model predicts a visual signal strength (VSS) and offers supporting information to help analysts assess model fit.

AI-assisted interviews promise to reduce respondent burden in surveys by allowing respondents to describe experiences naturally while an AI system noisily maps those accounts into structured survey variables. That mapping is a measurement process that is fallible, versioned, adaptive, and potentially behaves differently across subgroups. This paper proposes Adaptive Matrix Validation (AMV), a design in which each respondent completes an AI-assisted interview, which is then mapped into tabular data by the AI. Respondents are also asked a small, randomized set of structured questions, which are used for statistical adjustment. The estimator first calibrates the mapped values using validation answers from other respondents, then corrects the remaining error with the validation answers observed for the target respondent. The paper develops estimators for item means, subgroup estimates, and regression coefficients when outcomes, predictors, or both are mapped from interviews. It also gives planning formulas the number of validation questions required and the sample size. A design-calibration simulation, an American Time Use Survey emulation, and a CHAMPS verbal-autopsy narrative study show when sparse validation can improve precision and when it cannot

We address the problem of causal effect estimation in the presence of hidden confounders, using nonparametric instrumental variable (IV) regression. A leading strategy employs spectral features - that is, learned features spanning the top eigensubspaces of the operator linking treatments to instruments. We derive a generalization error bound for a two-stage least squares estimator based on spectral features, and gain insights into the method's performance and failure modes. We show that performance depends on two key factors, leading to a clear taxonomy of outcomes. In a good scenario, the approach is optimal. This occurs with strong spectral alignment, meaning the structural function is well-represented by the top eigenfunctions of the conditional operator, coupled with this operator's slow eigenvalue decay, indicating a strong instrument. Performance degrades in a bad scenario: spectral alignment remains strong, but rapid eigenvalue decay (indicating a weaker instrument) demands significantly more samples for effective feature learning. Finally, in the ugly scenario, weak spectral alignment causes the method to fail, regardless of the eigenvalues' characteristics.