Statistics Seminar: STA 290
Thursday, January 10th, 2013 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments 3:30pm, prior to seminar in MSB 4110 (Statistics Lounge)
Speaker: Lingzhou Xue University of Princeton
Title: "Regularized Learning of High-dimensional Sparse Graphical Models"
Abstract: In this talk, I will talk about our recent efforts on exploring the large-scale networks of binary data and non-Gaussian data respectively. In the first part of this talk, I will present the nonconcave penalized composite conditional likelihood estimator for learning sparse Ising models. To handle the computational challenge, we design an efficient coordinate-minorization-ascent algorithm by taking advantage of coordinate-ascent and minorization-maximization principles. Strong oracle optimality and explicit convergence rate of the computed local solution are established in the high-dimensional setting. Our method is applied to study the HIV-1 protease structure, and we obtain scientifically sound discoveries. In the second part, I will present a unified regularized rank estimation scheme for efficiently estimating the inverse correlation matrix of the Gaussian copula model, which is used to build a graphical model with the non-Gaussian data. The Gaussian copula graphical model is more robust than the Gaussian graphical model while still retains the nice graphical interpretability of the latter. Proposed rank-based estimators achieve the optimal convergence rate as well as graphical model selection consistency, and behave like their oracle counterparts.