Mathematics Seminar Date: Thursday, 1 February 2024 Time: 3:30 PM Venue: NKN Hall Robustifying likelihoods by optimistically re-weighting data Miheer Dewaskar Duke University, USA. 01-02-24 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.
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