arXiv subjects

Alan H. Welsh

Publications and source records attributed to Alan H. Welsh.

6 recordsLinked to original sources

arXiv2025

Copula-enhanced Vision Transformer for high myopia diagnosis through OU UWF fundus images

The advancement of AI-assisted myopia screening necessitates the joint diagnosis of both-eye (OU) high myopia (HM) status and the prediction of axial length (AL). This clinical requirement introduces a complex mixed-type (binary-continuous) multitask learning task with bi-domain (OU) image covariates, giving rise to two key challenges: i) capture the inter-ocular asymmetry of OU images within a cutting-edge foundation model; ii) model and estimate the conditional dependence structure among mixed-type multivariate responses given image covariates. We address the challenges by: i) imposing residual adapters on the Vision Transformer foundation model to capture the OU similarity and heterogeneity simultaneously; ii) developing a four-dimensional copula loss that is implementable in PyTorch based on a latent variable expression for the Gaussian copula likelihood, and proposing a computationally efficient fast Monte Carlo Expectation Maximization (fMCEM) algorithm to estimate copula parameters. We further formulate a specific overfitting problem called stronger covariance phenomenon in multitask learning. We reveal the disturbance of the phenomenon to estimation of copula parameters and theoretically demonstrate the numerical stability of the proposed fMCEM algorithm against the disturbance. The application to our annotated OU ultra-widefield fundus image dataset and simulation on synthetic data demonstrate that our method stably enhances the predictive capabilities on both classification and regression tasks.

cs.CV↗

arXiv2024

Robust Linear Mixed Models using Hierarchical Gamma-Divergence

Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction of random effects if the data are contaminated. We propose a new approach to robust estimation and inference for LMMs using a hierarchical gamma-divergence, which offers an automated, data-driven approach to downweight the effects of outliers occurring in both the error and the random effects, using normalized powered density weights. For estimation and inference, we develop a computationally scalable minorization-maximization algorithm for the resulting objective function, along with a clustered bootstrap method for uncertainty quantification and a Hyvarinen score criterion for selecting a tuning parameter controlling the degree of robustness. Under suitable regularity conditions, we show the resulting robust estimates can be asymptotically controlled even under a heavy level of (covariate-dependent) contamination. Simulation studies demonstrate hierarchical gamma-divergence consistently outperforms several currently available methods for robustifying LMMs. We also illustrate the proposed method using data from a multi-center AIDS cohort study.

stat.ME↗

arXiv2024

Restricted maximum likelihood estimation in generalized linear mixed models

Restricted maximum likelihood (REML) estimation is a widely accepted and frequently used method for fitting linear mixed models, with its principal advantage being that it produces less biased estimates of the variance components. However, the concept of REML does not immediately generalize to the setting of non-normally distributed responses, and it is not always clear the extent to which, either asymptotically or in finite samples, such generalizations reduce the bias of variance component estimates compared to standard unrestricted maximum likelihood estimation. In this article, we review various attempts that have been made over the past four decades to extend REML estimation in generalized linear mixed models. We establish four major classes of approaches, namely approximate linearization, integrated likelihood, modified profile likelihoods, and direct bias correction of the score function, and show that while these four classes may have differing motivations and derivations, they often arrive at a similar if not the same REML estimate. We compare the finite sample performance of these four classes, along with methods for REML estimation in hierarchical generalized linear models, through a numerical study involving binary and count data, with results demonstrating that all approaches perform similarly well reducing the finite sample size bias of variance components. Overall, we believe REML estimation should more widely adopted by practitioners using generalized linear mixed models, and that the exact choice of which REML approach to use should, at this point in time, be driven by software availability and ease of implementation.

stat.ME↗

arXiv2019

Finite sample properties of the Buckland-Burnham-Augustin confidence interval centered on a model averaged estimator

We consider the confidence interval centered on a frequentist model averaged estimator that was proposed by Buckland, Burnham & Augustin (1997). In the context of a simple testbed situation involving two linear regression models, we derive exact expressions for the confidence interval and then for the coverage and scaled expected length of the confidence interval. We use these measures to explore the exact finite sample performance of the Buckland-Burnham-Augustin confidence interval. We also explore the limiting asymptotic case (as the residual degrees of freedom increases) and compare our results for this case to those obtained for the asymptotic coverage of the confidence interval by Hjort & Claeskens (2003).

stat.ME↗

arXiv2017

A Copula-based Imputation Model for Missing Data of Mixed Type in Multilevel Data Sets

We propose a copula based method to handle missing values in multivariate data of mixed types in multilevel data sets. Building upon the extended rank likelihood of \cite{hoff2007extending} and the multinomial probit model, our model is a latent variable model which is able to capture the relationship among variables of different types as well as accounting for the clustering structure. We fit the model by approximating the posterior distribution of the parameters and the missing values through a Gibbs sampling scheme. We use the multiple imputation procedure to incorporate the uncertainty due to missing values in the analysis of the data. Our proposed method is evaluated through simulations to compare it with several conventional methods of handling missing data. We also apply our method to a data set from a cluster randomized controlled trial of a multidisciplinary intervention in acute stroke units. We conclude that our proposed copula based imputation model for mixed type variables achieves reasonably good imputation accuracy and recovery of parameters in some models of interest, and that adding random effects enhances performance when the clustering effect is strong.

stat.ME↗

arXiv2015

The Performance of the Turek-Fletcher Model Averaged Confidence Interval

We consider the model averaged tail area (MATA) confidence interval proposed by Turek and Fletcher, CSDA, 2012, in the simple situation in which we average over two nested linear regression models. We prove that the MATA for any reasonable weight function belongs to the class of confidence intervals defined by Kabaila and Giri, JSPI, 2009. Each confidence interval in this class is specified by two functions b and s. Kabaila and Giri show how to compute these functions so as to optimize these intervals in terms of satisfying the coverage constraint and minimizing the expected length for the simpler model, while ensuring that the expected length has desirable properties for the full model. These Kabaila and Giri "optimized" intervals provide an upper bound on the performance of the MATA for an arbitrary weight function. This fact is used to evaluate the MATA for a broad class of weights based on exponentiating a criterion related to Mallows' C_P. Our results show that, while far from ideal, this MATA performs surprisingly well, provided that we choose a member of this class that does not put too much weight on the simpler model.

stat.ME↗