A central issue in modern statistics and machine learning is overfitting. Many successful techniques have been developed under this mathematical framework known as regularization, which penalizes or adds constraints on the underlying model parameters to avoid overfitting. This project focuses on a Bayesian framework for effective regularization. The Bayesian framework is especially appealing for many applications since it provides a conceptually easy but principled way to coherently incorporate prior assumptions/knowledge, address overfitting and quantify uncertainty. The main goal of this project is to develop fast and scalable computational tools, as well as providing theoretical guarantees, to assist with the implementation of Bayesian inference for practical problems arising in many application areas.
This project focuses on a Bayesian framework for learning dependence structures among a large number of variables. In particular, the PI will develop a unified framework for Bayesian regularization for conditional Gaussian graphical models, mixed graphical models, and latent graphical models. The proposed research focuses on designing a family of sparsity inducing priors, deriving efficient algorithms to explore the posterior modes and to approximate the posterior distribution, and providing theoretical guarantees such as estimation error bounds and selection consistency for the obtained estimators. The proposed activities will generate research results that will be immediately applicable to many other statistical models beyond graphical models, and computation tools that will be made available via open-source statistical software packages in R and/or Python.
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.
