Iterative testing procedures and high-dimensional scaling limits of extremal random structures

University Of North Carolina At Chapel Hill, Chapel Hill NC

Investigators

Abstract

Over the past ten years, networks and network models have seen increasing use and importance in a variety of fields, including economics, neuroscience, genomics, and biomedicine. Work in these fields has driven an increase in statistical research concerning modeling of, and inference about, complex networks. The PIs will pursue several new directions in statistical network research, a key theme being the application and extension of recent work in probability on the theory of complex, random and geometric networks. In particular, the PIs will develop iterative testing methods to identify relational changes in large data sets, and to enhance the power of genomic studies that link genetic variation to global changes in gene expression. They will extend existing probabilistic techniques to provide theoretical support for the iterative testing procedure, and to address broader statistical questions concerning inference about complex associations between the features of large, high dimensional data sets. Methodological development and application will be carried out in cooperation with researchers in genomics, biomedicine, and sociology at UNC, with whom the PI and co-PI have long standing collaborations. Motivated in large part by the increasing use and importance of networks in a variety of fields, there has been a great deal of work in the statistics community devoted to the problem of testing and estimating associations between variables in high dimensional data sets. Concurrent with this statistical activity, recent developments in the fields of probabilistic combinatorics have significantly advanced our understanding of discrete random structures that capture the association of high-dimensional objects. The PIs will bring a number of these probabilistic tools to bear on association based inference problems. In particular, the PIs will develop and implement an iterative testing procedure that identifies self-associated sets of vertices in a graph, and self-associated sets of variables in a high dimensional data set. Within the framework of the iterative testing procedure they will develop computationally efficient methods for several applied problems: mining of block correlation differences in two sample studies, and identifying groups of mutually correlated variables in studies where each sample is assessed with two or more measurement platforms. As a special case of the latter problem, they will develop tools to enhance the power of genomic studies that link local genetic variation to global changes in gene expression. A second component of the proposed research is to adapt and extend existing techniques in probabilistic combinatorics to provide supporting theory for the iterative testing procedure, and to address broader statistical questions concerning the testing and estimation of correlations. Development and application of the methods will be carried out in cooperation with researchers in genomics, biomedicine, and sociology at UNC, with whom the PI and co-PI have long standing collaborations.