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Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to…

We propose a novel quantile function-based approach for neuroimaging classification using Wasserstein-Fr\'echet regression, specifically applied to the detection of mild traumatic brain injury (mTBI) based on the MEG and MRI data.…

Analysis of brain imaging scans is critical to understanding the way the human brain functions, which can be leveraged to treat injuries and conditions that affect the quality of life for a significant portion of the human population. In…

The goal of Bayesian deep learning is to provide uncertainty quantification via the posterior distribution. However, exact inference over the weight space is computationally intractable due to the ultra-high dimensions of the neural…

Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only…

We present a novel algorithm that is based on a Bayesian Markov Chain Monte Carlo (MCMC) technique for performing robust profile analysis of a data cube from either single-dish or interferometric radio telescopes. It fits a set of models…

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…

Detecting shared neural activity from functional magnetic resonance imaging (fMRI) across individuals exposed to the same stimulus can reveal synchronous brain responses, functional roles of regions, and potential clinical biomarkers.…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Magnetic resonance imaging (MRI) is the method of choice for noninvasive studies of micrometer-scale structures in biological tissues via their effects on the time/frequency-dependent ("restricted") and anisotropic self-diffusion of water.…

This paper studies the statistical model of the non-centered mixture of scaled Gaussian distributions (NC-MSG). Using the Fisher-Rao information geometry associated to this distribution, we derive a Riemannian gradient descent algorithm.…

In this paper, we propose a method for denoising diffusion-weighted images (DWI) of the brain using a convolutional neural network trained on realistic, synthetic MR data. We compare our results to averaging of repeated scans, a widespread…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

Accurate diagnosis of psychiatric disorders plays a critical role in improving the quality of life for patients and potentially supports the development of new treatments. Many studies have been conducted on machine learning techniques that…

Diffusion-weighted magnetic resonance imaging (DW-MRI) is a critical imaging method for capturing and modeling tissue microarchitecture at a millimeter scale. A common practice to model the measured DW-MRI signal is via fiber orientation…

Mapping from functional connectivity (FC) to structural connectivity (SC) can facilitate multimodal brain network fusion and discover potential biomarkers for clinical implications. However, it is challenging to directly bridge the reliable…

The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random…

MRI and CT are most widely used medical imaging modalities. It is often necessary to acquire multi-modality images for diagnosis and treatment such as radiotherapy planning. However, multi-modality imaging is not only costly but also…

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…

Decoding human brain activities via functional magnetic resonance imaging (fMRI) has gained increasing attention in recent years. While encouraging results have been reported in brain states classification tasks, reconstructing the details…