CS01: Advanced Bayesian Methods and Statistical Innovations in High-Dimensional Mixed-Type Data Analysis and Neuroimaging

Organizer: Hsin-Hsiung Huang (University of Central Florida)

Bayesian Sparse Kronecker Product Decomposition for Multi-task Mixed-effects Regression with Tensor Predictors

Hsin-Hsiung

We propose a novel Bayesian framework for jointly modeling continuous and binary responses with ultrahigh‑dimensional, low‑rank tensor predictors. The method embeds a Sparse Kronecker Product Decomposition (SKPD) of the coefficient tensor within the two‑step MtMBSP strategy—sure screening followed by refitted posterior sampling. Each coefficient tensor is expressed through a Tucker expansion composed of sparse Kronecker products, and parsimony is induced by Truncated Poisson–Binomial–Normal (TPBN) shrinkage priors. Posterior inference is performed by an efficient Polya–Gamma‑augmented Gibbs sampler. We prove that SKPD‑MtMBSP preserves the sure‑screening property and achieves posterior contraction even when the number of tensor elements \(p\) grows exponentially with sample size \(n\). Simulations and analyses of ADNI and OASIS MRI data demonstrate high predictive accuracy for both and binary responses while reliably recovering the underlying brain image tensor structure under extreme dimensionality.

Low-rank regularization of Fréchet regression models for distribution function response

Kyunghee Han

Fréchet regression has emerged as a useful tool for modeling non-Euclidean response variables associated with Euclidean covariates. In this work, we propose a global Fréchet regression estimation method that incorporates low-rank regularization. Focusing on distribution function responses, we demonstrate that leveraging the low-rank structure of the model parameters enhances both the efficiency and accuracy of model fitting. Through theoretical analysis of the large-sample properties, we show that the proposed method enables more robust modeling and estimation than standard dimension reduction techniques. We also present numerical experiments that evaluate the finite-sample performance to support our findings.