Regressing Multivariate Gaussian Distribution on Vector Covariates for Co-expression Network Analysis

Explore a comprehensive lecture on regressing multivariate Gaussian distribution on vector covariates for co-expression network analysis. Delve into the analysis of population-level single-cell gene expression data, which enables the construction of cell-type- and individual-specific gene co-expression networks through covariance matrix estimation. Examine the importance of understanding how these co-expression networks are associated with individual-level covariates. Learn about Fréchet regression with multivariate Gaussian distribution as an outcome and vector covariates, utilizing Wasserstein distance between distributions. Discover the test statistic based on Fréchet mean and covariate weighted Fréchet mean, and understand its asymptotic distribution under simultaneously diagonalizable covariance matrices. Gain insights into the application of this test statistic for assessing associations between covariance matrices and covariates, including the use of permutation for statistical significance. Review simulation results demonstrating correct type 1 error and adequate power of the proposed test. Conclude with an analysis of large-scale single-cell data, revealing the association between gene co-expression networks in the nutrient sensing pathway and age, highlighting perturbed gene co-expression networks in aging individuals.