arXiv preprints from January 1, 2026 through September 9, 2026 — 04:08:00 EST
The discovery of massive galaxies at redshifts $z\gtrsim10$ by the James Webb Space Telescope (JWST) has renewed interest in cosmological mechanisms capable of enhancing early structure formation while preserving the successful large-scale predictions of the standard $Λ$CDM model. We investigate a phenomenological scenario in which an...
It is known that the attractive singular inverse-square potential gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical results which demonstrate suppression of the collapse, caused by this singular potential, and the creation of the...
Spatial statistics has grown from kriging for spatial prediction into a broad framework for learning from complex dependent data. This article traces that development from random fields and spectral methods to Bayesian hierarchical models and scalable computation. It then connects these foundations to Spatial AI, where graph learning...
Decision tree-based models are widely used in machine learning due to their interpretability and strong empirical performance. However, training decision trees can be computationally expensive, particularly for large and high-dimensional datasets, largely due to the exhaustive search over candidate splits at each node. To improve...
This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data...
Autism spectrum disorder (ASD) is associated with heterogeneous alterations across distributed brain systems, creating challenges for whole-connectome inference. The difficulty arises not only from the large number of connections, but also from dependence among effects indexed by anatomically and functionally related region pairs. We...
Practitioners inferring causality from observational data usually rely on a single method and treat its output as causal truth. Recent tools select an optimal method for a dataset, and recent ensembles aggregate multiple causal-discovery algorithms into one graph, but little work pools evidence across different mathematical...
Classical information criteria such as the Bayesian Information Criterion (BIC) rely on regularity assumptions that break down for singular models, leading to incorrect model selection in settings such as deep learning. The Widely Applicable Bayesian Information Criterion (WBIC) relies on local learning coefficients $λ$, which in the...
We study inference-time control for text generation in discrete diffusion language models, where the goal is to steer sampling toward sequence-level rewards without retraining. Prior work in this domain has focused on particle-based methods such as best-of-$n$ sampling and bootstrap sequential Monte Carlo, which may suffer from...
Propensity score methods for causal inference are increasingly being used in cohort and experimental designs, but their development and uptake in outcome-dependent sampling schemes, such as case-control studies, remains limited. Case-control studies involve the sampling of individuals with and without an outcome of interest with the...
Environmental conditions are major drivers of malaria transmission, but epidemiological analyses are often constrained by temporal misalignment between health outcomes reported at coarse time scales and environmental exposures available at finer resolutions. Conventional approaches aggregate environmental data to match health...
Timely, paddock-scale estimates of plant-available water (PAW) can support crop management in water-limited grain systems. We present the Sydney Soil Water-Energy Balance (SWEB) model, a scalable, physically consistent modelling framework that integrates satellite and climate data with soil properties to estimate crop...
Probability estimation over large alphabets under log loss is a well-studied problem, with celebrated methods such as the Good-Turing estimator. We introduce and study a new Bayesian estimator with four notable properties. First, its construction is exceptionally simple: multiply independent uniform draws from the probability simplex...
In fixed-confidence best-arm identification, proofs often use a union bound across the competing arms. From a multiple-testing point of view this can look puzzling: if the best arm is unique, only one hypothesis of the form ``arm $i$ is best'' can be true. Why then should there be a Bonferroni-type factor of $K-1$? The answer is that...
This document describes the application of a first order linearised nonlinear repeated measurements approach to the analysis of battery cell ageing profiles generated under controlled conditions in a laboratory. The primary advantage of the model is it reflects the obvious structure in the data. Consequently, it is a two-component of...
We study a function-on-function linear regression model in which the response at time $t$ depends on both the past trajectory of a predictor and its concurrent value. The model combines an $L^2$-historical effect with a point-evaluation effect, and these two coefficient functions are not automatically identifiable. We characterize the...
We develop a partial identification learning framework for individualized treatment rules (ITRs) with categorical treatments, outcomes, and instrumental variables. Rather than relying on strong causal assumptions required for point identification, our framework leverages causal bounds to characterize the optimal treatment decision....
Predicting combinatorial effects from limited-range observations is a fundamental challenge in many scientific domains, including drug discovery and hyperparameter optimization. We study combinatorial extrapolation, where training data consists of axis-aligned samples with only one active covariate, while test-time inputs involve...
Reliability set estimation identifies input regions where a response probability exceeds a target level, bridging estimation and safety-critical decisions. Practitioners typically start with a working model, an imperfect approximation of the true response surface. Relying on this imperfect model may incur decision risk, potentially...
Instrumental variable (IV) methods are powerful for causal effect estimation with unmeasured confounding, but in practice researchers often face a set of candidate IVs whose validity is difficult to determine from observational data. This paper studies the problem of testing the validity of IV sets under Causal Additive Models with...
Skchange is an open-source Python library for detecting structural changes in time series. It implements modern change detection algorithms within a unified and extensible framework. The algorithms are modular and composable, and they include changepoint search methods based on both cost minimisation and statistical tests. Key...
A minibatch can influence training beyond the update at which it is observed because AdamW stores past gradient information in its optimizer states. We study this delayed effect through paired trajectories that differ only in one gradient update and share the same subsequent training sequence. We formulate AdamW as a finite-horizon...
We study heterogeneous treatment-effect (HTE) estimation in observational survival studies commonly associated with both censored outcomes and unmeasured confounding. We integrate causal survival forests (CSF) with negative controls (NC) from proximal causal inference and introduce Negative Control Causal Survival Forests (NC-CSF), a...
Predictive models over structured electronic health records (EHRs) remain central to machine learning for healthcare, but few have jointly emphasized quantitative laboratory information and interpretability with respect to input medical events. We present BERT-LER, a BERT-style model for coded EHR timelines pretrained and fine-tuned...
Mid-training is increasingly recognized as a critical stage for shaping the capabilities of large language models. Recent work has shown that targeted mid-training can strengthen reasoning-intensive abilities such as math and science, and can also improve agentic capabilities in software-engineering settings. In this work, we study...