Related papers: Estimating Models with High-Order Noise Dynamics U…
The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is…
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
Noise Contrastive Estimation (NCE) is a powerful parameter estimation method for log-linear models, which avoids calculation of the partition function or its derivatives at each training step, a computationally demanding step in many cases.…
Missing data is an universal problem in statistics. We develop a unified framework for estimating parameters defined by general estimating equations under a missing-at-random (MAR) mechanism, based on generalized entropy calibration…
The estimation of parameter standard errors for semi-variogram models is challenging, given the two-step process required to fit a parametric model to spatially correlated data. Motivated by an application in the social-epidemiology, we…
We propose self-adaptive training---a new training algorithm that dynamically corrects problematic training labels by model predictions without incurring extra computational cost---to improve generalization of deep learning for potentially…
State estimators often provide self-assessed uncertainty metrics, such as covariance matrices, whose credibility is critical for downstream tasks. However, these self-assessments can be misleading due to underlying modeling violations like…
Maximizing the computational utility of near-term quantum processors requires predictive noise models that inform robust, noise-aware compilation and error mitigation. Conventional models often fail to capture the complex error dynamics of…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
With a finite amount of measurement data acquired in variational quantum algorithms, the statistical benefits of several optimized numerical estimation schemes, including the scaled parameter-shift (SPS) rule and finite-difference (FD)…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
Frozen Vision Foundation Models (VFMs) with lightweight classification heads are increasingly used in medical imaging because they offer efficient and reproducible deployment. Yet noisy-label learning methods for this frozen-feature regime…
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…
We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…
Nonlinear Mixed Effects models (NLME) models are widely used in pharmacometrics and related fields to analyze hierarchical and longitudinal data. However, as the number of parameters and random effects increases, traditional methods for…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward…