Mapping covariance in brain FDG uptake to structural connectivity

Purpose Inter-subject covariance of regional 18F-fluorodeoxyglucose (FDG) PET measures (FDGcov) as proxy of brain connectivity has been gaining an increasing acceptance in the community. Yet, it is still unclear to what extent FDGcov is underlied by actual structural connectivity via white matter fiber tracts. In this study, we quantified the degree of spatial overlap between FDGcov and structural connectivity networks. Methods We retrospectively analyzed neuroimaging data from 303 subjects, both patients with suspected neurodegenerative disorders and healthy individuals. For each subject, structural magnetic resonance, diffusion tensor imaging, and FDG-PET data were available. The images were spatially normalized to a standard space and segmented into 62 anatomical regions using a probabilistic atlas. Sparse inverse covariance estimation was employed to estimate FDGcov. Structural connectivity was measured by streamline tractography through fiber assignment by continuous tracking. Results For the whole brain, 55% of detected connections were found to be convergent, i.e., present in both FDGcov and structural networks. This metric for random networks was significantly lower, i.e., 12%. Convergent were 80% of intralobe connections and only 30% of interhemispheric interlobe connections. Conclusion Structural connectivity via white matter fiber tracts is a relevant substrate of FDGcov, underlying around a half of connections at the whole brain level. Short-range white matter tracts appear to be a major substrate of intralobe FDGcov connections.

On the Solution of ℓ0-Constrained Sparse Inverse Covariance Estimation Problems

The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ1 regularizer to encourage sparsity is common practice, the combinatorial ℓ0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ0 constraint. We introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ0-constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods. Summary of Contribution: The inverse covariance estimation problem underpins many domains, including statistics, operations research, and machine learning. We propose a scalable optimization algorithm for solving the nonconvex ℓ0-constrained problem.

Disentangling microbial associations from hidden environmental and technical factors via latent graphical models

Detecting community-wide statistical relationships from targeted amplicon-based and metagenomic profiling of microbes in their natural environment is an important step toward understanding the organization and function of these communities. We present a robust and computationally tractable latent graphical model inference scheme that allows simultaneous identification of parsimonious statistical relationships among microbial species and unobserved factors that influence the prevalence and variability of the abundance measurements. Our method comes with theoretical performance guarantees and is available within the SParse InversE Covariance estimation for Ecological ASsociation Inference (SPIEC-EASI) framework (‘SpiecEasi’ R-package). Using simulations, as well as a comprehensive collection of amplicon-based gut microbiome datasets, we illustrate the method’s ability to jointly identify compositional biases, latent factors that correlate with observed technical covariates, and robust statistical microbial associations that replicate across different gut microbial data sets.