An official website of the United States government
Abstract A Bayesian method is proposed for variable selection in high-dimensional matrix autoregressive models which reflects and exploits the original matrix structure of data to (a) reduce dimensionality and (b) foster interpretability of multidimensional relationship structures. A compact form of the model is derived which facilitates the estimation procedure and two computational methods for the estimation are proposed: a Markov chain Monte Carlo algorithm and a scalable Bayesian EM algorithm. Being based on the spike-and-slab framework for fast posterior mode identification, the latter enables Bayesian data analysis of matrix-valued time series at large scales. The theoretical properties, comparative performance, and computational efficiency of the proposed model is investigated through simulated examples and an application to a panel of country economic indicators.
more »
« less
A Bayesian complex-valued latent variable model applied to functional magnetic resonance imaging
Abstract In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data.
more »
« less
- Award ID(s):
- 2210686
- PAR ID:
- 10542277
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series C: Applied Statistics
- Volume:
- 74
- Issue:
- 1
- ISSN:
- 0035-9254
- Format(s):
- Medium: X Size: p. 100-125
- Size(s):
- p. 100-125
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Networks throughout physics and biology leverage spatiotemporal dynamics for computation. However, the connection between structure and computation remains unclear. Here, we study a complex-valued neural network (cv-NN) with linear interactions and phase-delays. We report the cv-NN displays sophisticated spatiotemporal dynamics, which we then use, in combination with a nonlinear readout, for computation. The cv-NN can instantiate dynamics-based logic gates, encode short-term memories, and mediate secure message passing through a combination of interactions and phase-delays. The computations in this system can be fully described in an exact, closed-form mathematical expression. Finally, using direct intracellular recordings of neurons in slices from neocortex, we demonstrate that computations in the cv-NN are decodable by living biological neurons as the nonlinear readout. These results demonstrate that complex-valued linear systems can perform sophisticated computations, while also being exactly solvable. Taken together, these results open future avenues for design of highly adaptable, bio-hybrid computing systems that can interface seamlessly with other neural networks.more » « less
-
Abstract Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data.more » « less
-
Identifying Structural Brain Networks from Functional Connectivity: A Network Deconvolution ApproachWe address the problem of identifying structural brain networks from signals measured by resting-state functional magnetic resonance imaging (fMRI). To this end, we model functional brain activity as graph signals generated through a linear diffusion process on the unknown structural network. While this is admittedly an oversimplification of the complex mechanisms at work in the brain, recent studies have shown it is an accurate generative model for the second-order statistics of functional signals. We show the diffusion model implies that the signal covariance matrix (a.k.a. functional connectivity) is an unknown polynomial function of the structural network’s adjacency matrix. Accordingly, we advocate a network deconvolution approach whereby we: (i) use the fMRI signals to estimate the eigenvectors of the structural network from those of the empirical covariance; and (ii) solve a convex, sparsity-regularized inverse problem to recover the eigenvalues that were obscured by diffusion. The inferred structural networks capture some key patterns that match known pathology in attention deficit/hyper activity disorder. We also offer preliminary evidence supporting their role as potential biomarkers for subject diagnosis and classification.more » « less
-
Abstract In this article, we focus on estimating the joint relationship between structural magnetic resonance imaging (sMRI) gray matter (GM), and multiple functional MRI (fMRI) intrinsic connectivity networks (ICNs). To achieve this, we propose a multilink joint independent component analysis (ml‐jICA) method using the same core algorithm as jICA. To relax the jICA assumption, we propose another extension called parallel multilink jICA (pml‐jICA) that allows for a more balanced weight distribution over ml‐jICA/jICA. We assume a shared mixing matrix for both the sMRI and fMRI modalities, while allowing for different mixing matrices linking the sMRI data to the different ICNs. We introduce the model and then apply this approach to study the differences in resting fMRI and sMRI data from patients with Alzheimer's disease (AD) versus controls. The results of the pml‐jICA yield significant differences with large effect sizes that include regions in overlapping portions of default mode network, and also hippocampus and thalamus. Importantly, we identify two joint components with partially overlapping regions which show opposite effects for AD versus controls, but were able to be separated due to being linked to distinct functional and structural patterns. This highlights the unique strength of our approach and multimodal fusion approaches generally in revealing potentially biomarkers of brain disorders that would likely be missed by a unimodal approach. These results represent the first work linking multiple fMRI ICNs to GM components within a multimodal data fusion model and challenges the typical view that brain structure is more sensitive to AD than fMRI.more » « less
