arXiv subjects

Jessica Bernard

Publications and source records attributed to Jessica Bernard.

3 recordsLinked to original sources

arXiv2026

A Bayesian Vertical Federated Learning Framework for Multivariate Reduced-Rank High-Dimensional Regression

Federated learning (FL) has emerged as a leading privacy-preserving framework for collaborative machine learning across decentralized environments. While considerable progress has been made in horizontal federated learning (HFL), where data with common features is distributed across sites, vertical federated learning (VFL), where sites share observations across distinct feature sets, remains less explored. Advancing Bayesian high-dimensional multivariate reduced-rank regression methods for VFL poses unique challenges: (a) stringent privacy regulations preventing local site data sharing, and (b) fitting local regressions overlooks essential modeling aspects like inter-variable correlations. In contrast HFL allows each site to fit a comparable model independently. We present a novel Bayesian VFL framework for multivariate high-dimensional reduced-rank regression, termed BayesVFLReg, which enables precise coefficient estimation while safeguarding both feature and response privacy. Participating sites use a shared random sketching matrix to compress local variables into privacy-preserving sketches. A central server collects these sketches where Bayesian multivariate reduced-rank regression uses Gaussian scale mixture priors. For feature selection, we introduce a single-step post-processing strategy based on mixture-model clustering of the absolute posterior coefficient means to distinguish signal from noise per response variable. BayesVFLReg is computationally scalable for large, high-dimensional datasets and facilitates efficient variable selection. Theoretically, we establish sharp non-asymptotic bounds on the posterior probability that the fitted density falls within a Hellinger ball centered at the true data-generating density. Comparative simulation studies and real-world data analyses show that BayesVFLReg reliably identifies sparse feature effects, even under feature correlation.

stat.ML↗

arXiv2026

Integrative Predictor-Dependent Learning of Network Data and Spatially Correlated Nodal Attributes for Multimodal Brain Imaging in Aging

This article introduces a predictor-dependent joint modeling framework for network data obtained from multiple subjects over a shared set of nodes with spatial co-ordinates and spatially correlated nodal attributes. The framework is highly flexible, allowing concurrent inference on nodes significantly associated with a predictor, spatial associations of nodal attributes and the regression relationship between a predictor and edge connecting a pair of nodes or a specific nodal attribute. Empirical results indicate a superior performance of the proposed approach due to accounting for network structure and spatial correlation in the data simultaneously. The methodology analyzes multimodal brain imaging data collected first-hand in the coauthor's Lifespan Cognitive and Motor Neuroimaging Laboratory, with a focus on integrating structural and functional information. It examines brain connectivity, represented as a connectome network across regions of interest (ROIs) derived from functional magnetic resonance imaging (fMRI), while also incorporating ROI-specific attributes obtained from structural MRI data, for each subject. Subject-specific aging-related features and spatial locations of ROIs are incorporated in the analysis. This framework facilitates robust inference on the associations between predictors and brain connectivity patterns, the spatial relationships among ROI-specific attributes, and the regression relationships involving edges or ROI-specific attributes with aging-related predictors. By integrating these diverse data sources, the approach provides a deeper understanding of the complex interplay between brain structure, function, aging-related changes, and external predictors. As a model-based Bayesian approach, it provides uncertainty quantification for all inferences, offering robust and reliable results, particularly in scenarios with limited sample size.

stat.AP↗

arXiv2026

A Bayesian Framework for Quantifying Association Between Functional and Structural Data in Neuroimaging

Structural and functional neuroimaging modalities provide complementary windows into brain organization: structural imaging characterizes neural tissue anatomy and microstructure, while functional imaging captures dynamic patterns of neural activity and connectivity. Together, they offer a more complete picture than either alone. Recent multimodal neuroimaging work has focused on joint modeling of structural and functional data, often assuming a strong association between them to improve prediction and interpretability. However, relatively little attention has been given to developing statistically principled frameworks for formally testing hypotheses about these associations. Existing approaches typically rely on simple correlation-based measures or heuristic integration strategies, which may fail to capture the complex dependencies inherent in neuroimaging data, particularly when functional data are represented as brain networks and structural data as region-specific anatomical measures. We address this gap by developing an explicit Bayesian hypothesis testing framework for quantifying associations between structural and functional neuroimaging data. Our approach constructs functional brain networks from fMRI data, then integrates them with structural measurements through a hierarchical Bayesian model. The Bayesian formulation naturally accommodates two types of datasets with different structures, incorporates prior knowledge, and yields full posterior uncertainty quantification. Through extensive empirical studies, we demonstrate that the proposed method achieves excellent performance in detecting associations under a wide range of settings, including varying signal-to-noise ratios, different numbers of brain regions, and diverse sets of structural imaging measures.

stat.ME↗