This week's Statistics Seminar speaker is Xi Luo from Brown University.
Talk Title: Algebraic Properties and Large Covariance Estimation
Covariance estimation can be used to reveal the relationships between multiple variables and to infer the underlying data-generating mechanisms. Popular and important approaches include optimizing (regularized) likelihood functions, especially in the high dimensional setting where the sample size is much smaller than the number of variables. Under this setting, I will describe two non-likelihood approaches for covariance and inverse covariance estimation respectively. These approaches exploit the algebraic properties of covariance matrices under lower dimensional constraints, such as sparsity and low rank. In this talk, I will focus on adapting to unknown sparsity and on recovering model structures. Finite sample convergence rates are also established. Numerical performance of these methods is demonstrated using simulated and real datasets.
Refreshments will be served after the seminar in 1181 Comstock Hall.