Abstract:

Our work is motivated by the need for inference after regularized estimation with high dimensional datasets that contain grouped covariates. As an example, consider applying a logistic Group LASSO to a dataset with a binary outcome and categorical predictors. How do we conduct selective inference in the estimated sparse model? This problem is challenging due to two reasons: (1) existing approaches for a polyhedral selection method do not apply to the Group LASSO because there is no easy description of the selection event; (2) our data is no longer normal. To solve this problem, we construct an asymptotic selective likelihood that uses extra randomization to obtain an easy to describe selection event. Our new approach provides selective inference using randomized Group LASSO estimators in likelihood models including generalized linear models, and in other general forms of estimation, such as quasi-likelihood estimation to include possible overdispersion, for example. 

This is based on joint work with Yiling Huang, Sarah Pirenne  and Gerda Claeskens.

Bio:

Snigdha Panigrahi is currently an Assistant Professor in Statistics, with a courtesy appointment at the Department of Biostatistics.  She received her PhD in Statistics from Stanford University in 2018, and has been at the University of Michigan since. Snigdha's research is focused on selective inference, which intersects with high dimensional statistics, large-scale inferences and machine learning. She has been awarded two NSF grants in Statistics to support her research work.