arXiv preprints from January 1, 2026 through September 5, 2026 — 03:28:22 EST
The Antarctic ice sheet is a major source of uncertainty in future sea-level projections, and physical simulators such as the PSU3D-ICE model are essential for studying its evolution. Calibrating them against observations is challenging: the simulator outputs and observed ice-thickness fields are high-dimensional, spatially dependent,...
We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $α\geq 0$ for polynomial inner-product kernels. We derive asymptotically sharp expressions for the kernel spectrum and the generalization error in the polynomial high-dimensional regime $n=Θ(d^κ)$, revealing...
Relational Event Models (REMs) provide valuable insights into the dynamics of longitudinal social networks. Yet, the vast availability of potential predictors for a dyad's event rate poses the risk of selecting irrelevant variables and specifying an overfitted model that does not generalize to new data. Despite the recent popularity...
Global goodness-of-fit and discrepancy statistics can establish that a sample departs from a reference distribution without identifying which observations drive the departure. We develop a framework for this localization problem by assigning to each observation its conditional or marginal contribution across random statistical...
This paper investigates whether five fold cross fitting improves nonresponse adjustment in survey estimation when flexible machine learning methods are used to estimate response propensities. We conduct a finite population Monte Carlo simulation with 90 experimental configurations and 2,000 replications per configuration, varying...
We extend the FLOP (fast learning of order and parents) algorithm recently proposed by Wienöbst et al. (2026) from observational to interventional data. In particular, we use the interventional BIC score of Hauser and Bühlmann (2012), adapting it to be used with the iterative Cholesky-based score updates that are partly responsible...
We study the non-uniqueness of exact two-sided $p$-values in continuous one-parameter natural exponential families (NEFs). For directed one-sided problems, the tail $p$-value agrees with the $p$-values using UMP, UMPU, and likelihood-ratio (LR) tests. For a two-sided simple null, we distinguish four constructions: equal-tail,...
We study risk-averse decision making, in which an agent selects actions while being uncertain about the true system state. The risk is measured via optimized certainty equivalent (OCE) metrics, which generalize popular criteria such as mean-variance risk and conditional value-at-risk (CVaR). We characterize the optimal policy under...
Modern time series are often long, serially dependent, and non-stationary. Existing change-point methods either target specific changes or become computationally intensive when using nonparametric costs on long series. Many also require thresholds to be carefully calibrated under serial dependence. We introduce SCAN, an offline method...
In this work, we explore particle learning strategies for the joint estimation of static parameters and latent states within conditional sequential Monte Carlo (CSMC) algorithms. Building on this idea, we propose the p(parameter)-CSMC algorithm, which incorporates both parameter learning and ancestor sampling, leading to much better...
Bayesian variable selection becomes computationally challenging when models contain many dependent parameters. We study Piecewise Deterministic Markov Process (PDMP) samplers as a continuous-time alternative to conventional Markov chain Monte Carlo for spike-and-slab variable selection. In sticky PDMP samplers, active parameters...
We propose a multivariate extension of the pseudo-Voigt profile-a weighted convex combination of Gaussian and Cauchy distributions-within a finite mixture modeling framework for robust model-based clustering and outlier detection. To ensure parsimony and coherence within clusters, shared location and scale parameters are imposed...
Aggregated relational data (ARD) record how many ties sampled respondents have to predeclared groups without revealing individual dyads. We ask whether such counts can falsify a pure additive-activity network model for one predeclared form of residual cross-group association. When the groups form an exhaustive partition, respondent...
Synthetic data can improve statistical inference when real data are scarce, but naively treating synthetic samples as real data can introduce bias and lead to unreliable inference. We develop a general framework for synthetic-augmented inference across a population of related tasks. It characterizes synthetic augmentation by the...
High-dimensional semilinear parabolic partial differential equations arise in stochastic control, financial engineering, and uncertainty quantification, but classical spatial discretizations suffer from the curse of dimensionality. Motivated by Gaussian perturbation and conditional regression in denoising score matching, we propose...
Three players won 66 of the 81 Grand Slam titles contested between 2003 and 2023, and their era is widely held to be the most dominant in the history of tennis. Assessing it means comparing players who never met, so that every comparison passes through the opponents each did face. We measure dominance by how far a player stands above...
Statistical tests are often asked to do too much. A single reported result is expected to describe what the observed data say, reassure readers about repeated-sampling behavior, and remain convincing when the working model is perturbed. Those tasks are connected, but they are not equivalent. Fisherian inductive inference and...
We establish a global finite-sample guarantee for synchronous quantile temporal-difference learning (QTD) in tabular distributional reinforcement learning. The proof separates two stability mechanisms. A global comparison argument, based on the order monotonicity of reward cumulative distribution functions and the $W_\infty$...
Music recommendation relies primarily on two signals: user-item interactions, which fail in the cold-start regime, and intrinsic musical content, available for any recording. We argue that a third, largely untapped signal is both richer and more principled: critical adjacency, the pairwise relation established when an expert critic...
Background/Aims: Adjustment for prognostic baseline covariates can improve precision in randomized trials. Previous work has shown that jointly modeling primary and secondary endpoints can yield additional precision by borrowing information across endpoints. We investigated whether these approaches can be combined to achieve...
Recursive application of the law of total variance decomposes the marginal variance of an outcome into components attributed to explanatory variables and a residual component. The resulting decomposition depends on the chosen conditioning order, and its components do not in general have causal interpretations. We develop a graph-based...
It is well known that the gap in life expectancy at birth can be seen as the net difference between two survivorship functions. When calculating the absolute difference between the two survivorship functions instead, we derive a distributional inequality measure which is called the Wasserstein distance. The measure quantifies how far...
We develop a log-Gaussian Cox process framework for modelling street-level crime data observed on a road network when the released event locations are spatially obfuscated. Motivated by UK Police street-level crime data, where published coordinates are anonymised proxy locations rather than exact event locations, we address the...
Many scientific and engineering applications require estimating unknown parameters from experimentally observable data -- an inverse problem that is inherently challenging due to nonlinearity, noise, and ill-posedness. In this paper, we propose an active diffusion-based inverse problem solver. A DM is trained to learn the mapping...
Joint analyses across multiple institutions are increasingly important in biomedical and epidemiological research, particularly for rare diseases where datasets are typical small. However, privacy regulations and institutional policies often prevent the sharing of individual-level patient data. In this paper we present an accurate and...