2021/10/13 by Ilias Moysidis, Bing Li, Moysidis, Ilias +1
Computer Science · Biochemistry, Genetics and Molecular Biology · Mathematics · #Bayesian Modeling and Causal Inference #Metabolomics and Mass Spectrometry Studies #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2110.06653
Functional graphical models explore dependence relationships of random processes. This is achieved through estimating the precision matrix of the coefficients from the Karhunen-Loeve expansion. This paper deals with the problem of estimating functional graphs that consist of the same random processes and share some of the dependence structure. By estimating a single graph we would be shrouding the uniqueness of different sub groups within the data. By estimating a different graph for each sub group we would be dividing our sample size. Instead, we propose a method that allows joint estimation of the graphs while taking into account the intrinsic differences of each sub group. This is achieved by a hierarchical penalty that first penalizes on a common level and then on an individual level. We develop a computation method for our estimator that deals with the non-convex nature of the objective function. We compare the performance of our method with existing ones on a number of different simulated scenarios. We apply our method to an EEG data set that consists of an alcoholic and a non-alcoholic group, to construct brain networks.