Statistics

This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain $[0,1]^d$ and $d$-dimensional compact Riemannian manifolds. We propose a novel constructive approximation framework for…

Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet…

Unlabeled data are increasingly prevalent in contemporary economic studies, yet their effective use for improving prediction remains challenging because the outcomes are often costly or even infeasible to observe. Machine learning methods…

We study solving large-scale fixed-point equation \(x^\star=\bar F(x^\star)\) with decomposition. Standard strict decomposition assigns each agent a disjoint block and evaluates updates using only owned coordinates. For most operators,…

We consider a broad class of semiparametric regression models in which the conditional distribution of the response takes the form $f\{Y|\bf{x}^{\rm T}\boldsymbol{\beta}+m(z), \phi\}$, which is known up to a parametric component…

Multi-institutional electronic health record (Multi-EHR) data have emerged as a powerful resource for developing predictive models to support clinical decisions and for generating reliable real-world evidence. By aggregating information…

Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs…

Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component recovery. We develop an asymptotically exact mean-field theory…

The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing…

Relative abundance, measured as the number of animals caught per unit of sampling effort (CPUE), is commonly used to monitor fish and wildlife populations, largely because sampling methods are cost-effective to implement. Modeling relative…

Human activity spaces are shaped by individual mobility and the built environment, motivating statistical methods that integrate GPS observations with GIS representations of places and routes. We propose a novel methodology to estimate…

We introduce the Sinkhorn treatment effect, an entropic optimal transport measure of divergence between counterfactual distributions. Unlike classical quantities such as the average treatment effect, this measure captures differences across…

Post-deployment monitoring of healthcare AI requires statistically valid, label-efficient methods, but gold-standard labels from clinician chart review are expensive. Prediction-powered inference (PPI) and active statistical inference (ASI)…

We propose and analyse rolling-origin conformal prediction for time-series forecasting. The method calibrates the conformal quantile against the $m$ most recent pseudo-out-of-sample forecast errors, adapting to serial dependence, volatility…

Pragmatic trials increasingly define outcomes using real-world data such as electronic health records, where assessments are collected during routine care rather than at fixed timepoints. Consequently, these uncontrolled assessments may be…

This paper proposes a time-warping transfer learning method, a technique for temporally rescaling the learned dynamics of a recurrent neural network (RNN) with a Long Short-Term Memory (LSTM) layer to enable task transfer across fuel…

Exposure characterization in regional risk assessment aims to assign physical properties to the assets of interest so they can be associated with damage and loss functions. While this process has benefited from the growing availability of…

This work studies decentralized novelty detection with global false discovery rate (FDR) control across heterogeneous composite null distributions, without sharing the raw data due to privacy and bandwidth considerations. We propose a…

We present a framework for the scale-invariance characterization of stochastic processes in reconstructed finite-dimensional phase spaces. This framework analyses the structural and dynamical properties of the phase space and is based on a…

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…