Name of the Seminar: Statistics and Probability Seminar

Day, date and time: Wednesday, 24 July 2024, 4:00 pm

Venue: Ramanujan hall

Host: Debraj Das

Speaker: Mihir Dewaskar

Affiliation: Duke University

Title: Robustifying likelihoods by optimistically re-weighting data

Abstract: Likelihood-based inferences have been remarkably successful in
wide-spanning application areas. However, even after due diligence in
selecting a good model for the data at hand, there is inevitably some
amount of model misspecification: outliers, data contamination, or
inappropriate parametric assumptions such as Gaussianity mean that most
models are at best rough approximations of reality. A significant
practical concern is that under large sample sizes, even small amounts of
model misspecification may have a substantial impact on our inferences. In
this talk, we discuss how one can robustly estimate likelihood-based
models by re-weighting terms in the likelihood. We term this as
"optimistic re-weighting" because the weights are chosen to make the
re-weighted data look like that arising from our model. We describe a
theoretically motivated alternating optimization procedure called
Optimistically Weighted Likelihood (OWL) to obtain these weights. We
describe two applications of OWL: first to estimate the average treatment
effect in a micro credit study in the presence of outliers, and second to
robustly fit a Gaussian mixture model to single cell RNA-Seq data.