Presentation: Shrinking Characteristics of Precision Matrix Estimators
Speaker: Aaron Molstad, Ph.D., Postdoctoral Research Fellow, Public Health Sciences Division, Fred Hutch
Abstract: In this talk, we propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative log-likelihood plus a penalty on a linear or affine function evaluated at the optimization variable corresponding to the precision matrix. We establish convergence rate bounds for these estimators and propose an alternating direction method of multipliers algorithm for their computation. Our simulation studies show that our estimators can perform better than competitors when they are used to fit predictive models. In particular, we illustrate cases where our precision matrix estimators perform worse at estimating the population precision matrix but better at prediction. Finally, we use our estimator to fit the linear discriminant analysis model which classifies patients with inflammatory bowel disease based on their gene expression profiles.