Every few days, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
The article featured today is from the Canadian Journal of Statistics, with the full article now available to read here.
Zhang, Q. (2020), Direct estimation of differential networks under high‐dimensional nonparanormal graphical models. Can J Statistics, 48: 187-203. doi:10.1002/cjs.11526
In genomics, it is often of interest to study the structural change of a biological pathway or a gene set between two populations, e.g., healthy vs cancerous subjects. Such information may provide functional insights into the pathogenesis of a disease. Assuming the data follow normal distributions, this problem can be transformed to estimating the difference between two precision matrices, and several approaches have been recently developed for this task such as joint graphical lasso and fused graphical lasso. However, the normality assumptions made in the existing approaches are often violated in real world applications. For instance, most of the RNA-Seq data do not follow normal distributions even after log-transformation or other variance-reducing transformations.
In this article, Zhang proposed a novel approach to directly estimate the structural change of a network under a more flexible framework, namely nonparanormal graphical model. Zhang proposed to use a novel method to estimate the structural change of a network based on the ranks of data, together with a fast algorithm. Theoretical properties of the new estimator are also established under a high-dimensional setting where the network size is much larger than sample size. Simulation study has shown that this method works well for both sparse and dense networks, with relatively low computational cost. In addition, the author applied the new method to study the structural difference of two genetic pathways between two cancer subtypes.