arXiv preprints from January 1, 2026 through September 10, 2026 — 03:19:34 EST
Bayesian optimal experimental design (BOED) aims to collect informative data by optimizing an expected utility reflecting the goals of an experiment. However, this optimization is computationally challenging for common utilities and complex models. This is especially so for sequential or adaptive designs, where design and data...
Problem-solving log process data from computer-based assessments provide detailed information about how respondents approach and complete tasks. However, the resulting action sequences are complex and noisy, making it difficult to identify specific behaviors associated with successful performance. This paper proposes a...
Statistical inverse problems have garnered significant attention in recent years due to the growing importance of statistical learning theory and functional analytic approaches in the fields of machine learning and artificial intelligence. In this paper, we investigate the stable approximation of the element $u^{\dagger}$ that...
Ornstein-Uhlenbeck processes with flexible multivariate drift matrices are powerful models for capturing coupled, asymmetric, and damped-oscillatory mean reversion. However, likelihood-based inference is challenging because the drift matrix must remain Hurwitz stable, while likelihood and gradient evaluations require repeated, costly...
Interference occurs when one individual's treatment or exposure affects another individual's outcome. In particular, we assume partial interference, where individuals are divided into groups such that there is no interference between individuals in different groups. In observational studies, inverse probability weighting (IPW) based...
The combination of traditional statistical models and neural network (NN) components into semi-structured hybrid models is an intriguing approach to construct models that, ideally, combine traditional interpretability with the unprecedented flexibility of NNs. In order to preserve interpretability, it is usually necessary to restrict...
In multi-institutional studies, different parties hold distinct feature blocks for partially overlapping sets of individuals. Responses may also be missing for some records. In such settings, we propose Assisted Learning with Block-Missing Data (ALB) for sparse high-dimensional linear estimation and coordinatewise inference without...
LLM judges are often evaluated with a single prompt and only a few repeated calls. When their verdicts vary, it remains unclear whether the variation comes from sampling noise within a prompt or systematic differences across prompts. We formalize this distinction using a second-order response law: the distribution of...
Aggregate accuracy hides where models succeed and fail. Estimating conditional performance profiles from gold labels alone is expensive, while cheap auxiliary signals such as LLM-judge scores, pairwise comparisons, confidence scores, and judge-disagreement features can be collected for every benchmark item but are often biased or...
We propose a regression model for the extreme tail of a response variable, in which covariates rescale the tail without changing its shape. A single covariate-dependent function then characterizes the entire conditional tail, in contrast to extreme quantile regression, which targets a quantile at a pre-specified level. The tail shape...
Identification of dominant polynomial-chaos modes is usually formulated as a sparse-regression problem on a sampled multivariate polynomial dictionary. We develop coded Hankel polynomial chaos (CH-PC), a complementary spectral formulation for dominant-mode identification. A finite generating transform converts PCE coefficients into a...
Coresets distill large datasets into small, representative subsets for efficient downstream learning. Yet Optimal Transport (OT)-based selection typically requires intensive computation of transport plans, limiting scalability. We introduce a scalable Sinkhorn coreset method that permits closed-form updates of the entropically...
Group Independent Component Analysis (gICA) is widely used to decompose high-dimensional functional MRI data into interpretable brain networks. However, conventional gICA primarily identifies components shared across subjects. This group-level assumption can limit the recovery of networks present only in individuals or subject...
Estimating high dimensional Generalized Structural Equation Models presents severe computational challenges. Traditional simultaneous estimators frequently suffer from numerical instability and prohibitive computational costs. Moreover, there are no tractable algorithms for families such as Poisson, negative binomial, and gamma. To...
Personalized predictive modelling has been growing rapidly with the increasing availability of Electronic Health Records. This approach aims to improve a model's predictive performance by fitting a unique model to each individual. We train the model on a subset of the training data consisting of individuals similar to the individual...
We initiate a polyhedral study of the graph multi-separator problem proposed by Irmai et al. (2024) as an alternative to the lifted multicut problem for application to the task of image segmentation. Starting with an integer linear program (ILP) formulation and the multi-separator polytope spanned by its feasible solutions, we...
Interconnected systems have been widely studied, with a focus on interconnected systems whose subsystems are solely input-to-state stable (ISS) or passive systems. The focus of this work is on the interconnected systems that appear in adaptive gradient methods. In adaptive gradient methods, one subsystem seeks to move parameters of a...
Let $H$ and $K$ be subgroups of a virtually polycyclic group $G$. We prove the Hirsch length inequality $$h(H)+h(K) \leq h(H\cap K)+h(G).$$ We show that equality holds when the number of $(H,K)$-double cosets is finite, and that the converse holds when $G$ is nilpotent. We also apply this to twisted conjugacy, showing that for...
This paper studies generalized Hamiltonian gradient flows for contact-type Hamilton--Jacobi equations, adopting the variational framework of Herglotz's principle and its fundamental solution \(h_L(t,x,y,u)\). Two main results are presented. First, precise first-order sensitivity relations are derived, linking derivatives of \(h_L\) to...
This paper provides a complete characterization of the sign of the propagation speed in the symmetric two-species Lotka-Volterra competition-diffusion model under strong competition. The system admits a unique bistable travelling front and the sign of its speed determines which of the two species invades the other. We prove that for...
We study quadratic polynomials that are nonnegative on the non-compact set \[ F:=\{(x_1,x_2)\in\mathbb R^2:\ x_1\ge 0,\ x_2\ge 0,\ x_1x_2\le 1\}. \] All extreme rays of the cone of nonnegative quadratic polynomials are characterized on this set. The characterization allows us to study parameterized valid inequalities for quadratic...
We obtain arithmetic conditions which are satisfied by solvable groups admitting an abelian $π$-subgroup. First, we extend a previous characterization by removing the square-free hypothesis on some fixed irreducible character degree. We then show the same arithmetic conditions follow from a faithful action of an abelian $π$-subgroup...
The aim of this manuscript is to show that the group of autoequivalences of an exact Courant algebroid over a compact base manifold is a tame Fréchet Lie group. Moreover, we compute its Lie algebra. Furthermore, we show that the space of generalized almost complex structures is a tame Fréchet manifold and that the canonical action of...
Battery-swapping stations (BSSs) can shorten electric-vehicle energy replenishment while using centrally managed battery inventories as flexible grid-connected storage. Realizing both benefits requires the station to schedule charging, grid discharge, and swapping service before future customer demand and electricity prices are known....
We establish the Moran--Hutchinson formula for attractors of finite systems of surjective similitudes on semimetric spaces. More precisely, for a complete, normal semimetric space satisfying strong regularity and geometric doubling, we prove that the open set condition implies that the Hausdorff measure of the attractor at the...