Statistical Learning for High-Dimensional Relational Data

Ohio State University, The, Columbus OH

Investigators

Abstract

Technological advances in data acquisition, digital observation, and storage have produced an explosion in high-dimensional datasets that are often too large and noisy for traditional data analysis tools. In many cases these high-dimensional datasets are transformed into relational data that summarize relations between pairs of entities in the original dataset. There are two major classes of statistical methods for analyzing such relational data: techniques from classical multivariate analysis and probabilistic graphical models. These two classes are often viewed as disparate yet complementary approaches to relational data analysis. However, both can fail from being overwhelmed by noise and high-dimensionality. This research project proposes a new framework that unifies these two classes of methods under the umbrella of regularized statistical learning, and it will address three important issues: (1) it will reveal important conceptual links between these disparate methods, thus providing a common ground for developing new and hybrid methods; (2) it will advance theoretical understanding of these methods especially in the case of high-dimensional and noisy data; (3) it will advance computational techniques that enable these methods to be applied to big data that is high-dimensional and large-scale. Statistical theory has shown that traditional multivariate methods can fail on high-dimensional data and that some form of regularization is necessary for estimation. Despite the recent surge in development of regularized methods, there still exists a gap between the methodological developments and theoretical understanding. This research project fills this gap by combining methodological development with theoretical insight to produce a unified family of regularized methods for relational data that are both computationally efficient and theoretically sound. The theoretical insights will reveal the statistical properties of the methods under very weak assumptions, and they will enable computational strategies that exploit hidden structure in the optimization problems underlying the methods.