Jianlei Huang | Searcharxiv

arXiv2026

A semiparametric approach for the estimation of covariate-adjusted area under the receiver operating characteristic curve

Receiver operating characteristic (ROC) and the area under the ROC curve (AUC) are widely used to evaluate the discriminative ability of biomarkers. In many clinical settings, however, diagnostic accuracy varies substantially across patient characteristics, and failure to account for such heterogeneity can lead to misleading conclusions. We propose a new semiparametric framework based on generalized additive models to estimate covariate-specific and covariate-adjusted AUC while allowing for nonlinear and interaction effects of covariates on biomarker performance. Our method accommodates both binary and multicategory disease status. We also establish the asymptotic properties of the proposed estimators. Simulations demonstrate favorable finite-sample performance. We illustrate the method using data from the Alzheimer's Disease Neuroimaging Initiative, where substantial heterogeneity in biomarker discrimination across covariates is observed.

stat.ME↗

arXiv2025

Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equations

Working with systems of partial differential equations (PDEs) is a fundamental task in computational science. Well-posed systems are addressed by numerical solvers or neural operators, whereas systems described by data are often addressed by PINNs or Gaussian processes. In this work, we propose Boundary Ehrenpreis--Palamodov Gaussian Processes (B-EPGPs), a novel probabilistic framework for constructing GP priors that satisfy both general systems of linear PDEs with constant coefficients and linear boundary conditions and can be conditioned on a finite data set. We explicitly construct GP priors for representative PDE systems with practical boundary conditions. Formal proofs of correctness are provided and empirical results demonstrating significant accuracy and computational resource improvements over state-of-the-art approaches.

stat.ML↗