The Department of Statistics Graduate Seminar Series Presents: Yanzhen Deng, Alexander Giessing, and Jun Guo

Yanzhen Deng "Gaussian Graphical Model with Vector-valued Nodes"
Abstract:
Gaussian graphical model (GGM) is widely used to reflect the dependence structure of a group of random variables. In this report, I will introduce our working progress on generalizing the classical GGM, so that each node in the graph represents a random vector instead of a random variable. We propose to estimate such high-level conditional independence graph using nodewise regression. In our setting, this regression has multivariate response and grouped covariates. The edges are decided by the block-wise sparsity of the coefficients, so we use a block-norm regularization to induce the sparsity we want. The success of graph estimation relies on the sparsity recovery of each regression, and our theory reveals under what conditions do we have exact and partial sparsity recovery for this type of regression.

Alexander Giessing "Minimum Predictive Risk Estimation in High-dimensional Misspecified Quantile Regression"
Abstract:
We introduce the concept of minimum predictive risk in misspecified quantile regression with a growing number of predictors. This framework is natural in situations in which the true quantile functions are unknown or stipulating the existence of a single true quantile function is too restrictive. We propose a nonparametric estimator of the minimum predictive risk and analyze its theoretical properties. Since “risk” is a ubiquitous quantity in statistics, our estimator is useful beyond estimating the (predictive) risk. In particular, we illustrate how our estimator can
be used for model selection and testing of (nested) quantile regression models for minimum predictive risk under misspecification. We provide numerical studies that support our theoretical analyses.

Jun Guo "Stochastic Non-convex Optimization in high dimensional Mixed Effect Generalized Linear Models"
Abstract:
In this report, I will introduce our study on several algorithms we have developed to solve the high dimensional mixed effect generalized linear models. Mixed effect generalized linear models are widely useful in modeling scientific and industrial data which involves large number of features of imbalanced influence to the outcome or heterogenous population. Due to the non-convexity and intractable and possibly high dimension integration in the model objective functions, inference for high dimensional mixed effect generalized linear models remains a very challenging problem. We have developed stochastic and deterministic approximation algorithms solving the model. We develop algorithm convergence theory and compare our algorithms with the only other existing (to the reporter's knowledge) estimator "glmmLasso" based on Laplace approximation and demonstrate our algorithm accuracy.