Latent variables models have become one of the most powerful tools in modern statistics and data science. They are indispensable in the core data-driven technologies responsible for advancing a vast array of domains of engineering and sciences. While these tools represent remarkable achievements in which statisticians have played fundamental and decisive roles, there are urgent and formidable challenges lying ahead. As these tools are increasingly applied to ever bigger data sets and systems, there are deep concerns that they may no longer be understood, nor is their construction and deployment reliable or robust. When treated as merely black-box modeling devices for fitting densities and curves, latent variable models are difficult to interpret and can be hard to detect or fix when something goes wrong, either when the model is severely misspecified or the learning algorithms simply break down. This project aims to address the theoretical and computational issues that arise in modern latent variable models, and the learning efficiency and interpretability of such statistical models when they are misspecified.
The goals of this project are to develop new methods, algorithms and theory for latent variable models. There are three major aims: (1) a statistical theory for parameter estimation that arises in latent variable models; (2) scalable parameter learning algorithms which account for the geometry of the latent structures, as well as the geometry of the data representation arising from specific application domains; and (3) impacts of model misspecification on parameter estimation motivating the development of new methods. These three broadly described aims are partly motivated by the PI's collaborative efforts with scientists and engineers in several data-driven domains, namely intelligent transportation, astrophysics and topic modeling for information extraction. In all these domains, latent variable models are favored as an effective approximation device, but practitioners are interested in not only predictive performance but also interpretability. In terms of methods and tools, this research draws from and contributes to several related areas including statistical learning, nonparametric Bayesian statistics and non-convex optimization. In terms of broader impacts, the development of scalable geometric and variational inference algorithms for latent variable models will help to expand the statistical and computational tool box that are indispensable in the analysis of complex and big data. The investigation into the geometry of singularity structures and the role of optimal transport based theory in the analysis of models and the development of algorithms will help to accelerate the cross-fertilization between statistics and mathematics, computer science and operations research. In terms of education and training, the interdisciplinary nature of this project provides an exciting opportunity to attract and train a generation of researchers and students in variational methods and optimization, statistics and mathematics, as well as machine learning and intelligent infrastructure. The materials developed in this project will be integrated into an undergraduate honor course and a summer school for statistical science and big data analytics developed at the University of Michigan.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
