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We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR…
Mediation analysis aims to separate the indirect effect through mediators from the direct effect of the exposure on the outcome. It is challenging to perform mediation analysis with neuroimaging data which involves high dimensionality,…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
The United States Bureau of Labor Statistics collects data using survey instruments under informative sampling designs that assign probabilities of inclusion to be correlated with the response. The bureau extensively uses Bayesian…
Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty…
This paper presents a Bayesian regression model relating scalar outcomes to brain functional connectivity represented as symmetric positive definite (SPD) matrices. Unlike many proposals that simply vectorize the matrix-valued connectivity…
Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…
A common analytical problem in neuroscience is the interpretation of neural activity with respect to sensory input or behavioral output. This is typically achieved by regressing measured neural activity against known stimuli or behavioral…
Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…
The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs…
Bayesian whole-brain functional magnetic resonance imaging (fMRI) analysis with three-dimensional spatial smoothing priors has been shown to produce state-of-the-art activity maps without pre-smoothing the data. The proposed inference…
Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…
Large spatiotemporal datasets are a challenge for conventional Bayesian models because of the cubic computational complexity of the algorithms for obtaining the Cholesky decomposition of the covariance matrix in the multivariate normal…
We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with…
Functional neuroimaging can measure the brain?s response to an external stimulus. It is used to perform brain mapping: identifying from these observations the brain regions involved. This problem can be cast into a linear supervised…
Working memory (WM) was one of the first cognitive processes studied with functional magnetic resonance imaging. With now over 20 years of studies on WM, each study with tiny sample sizes, there is a need for meta-analysis to identify the…
Brain-computer interfaces (BCIs), particularly the P300 BCI, facilitate direct communication between the brain and computers. The fundamental statistical problem in P300 BCIs lies in classifying target and non-target stimuli based on…
Single image super-resolution (SISR) aims to obtain a high-resolution output from one low-resolution image. Currently, deep learning-based SISR approaches have been widely discussed in medical image processing, because of their potential to…