Speaker: Shuvayan Banerjee (IIT Bombay)
Host: Radhendushka Srivastava
Title: Pre synopsis seminar
Time, day and date: 7:00:00 AM, Thursday, June 26
Venue: Online (https://meet.google.com/bby-rcae-wvz)
Abstract: This talk addresses the challenges of bias and model mismatch in sparse signal estimation, particularly within compressed sensing (CS)-based group testing frameworks. It is structured in three parts. First, we present a novel, closed-form solution for efficiently computing the debiasing matrix W for the LASSO estimator by reparameterizing the optimization problem originally posed by Javanmard and Montanari(2014). This approach preserves theoretical guarantees while avoiding the computational burden of estimating the debiasing matrix. In the second part, we introduce theOptimal Debiased Robust Lasso Test Method (ODrlt), a testing framework for identifying model mismatch errors (MMEs) in group testing, which integrates debiased estimation with dual hypothesis testing to detect defective samples and mis-specified groups. We provide theoretical error bounds and demonstrate superior performance over baseline methods. The final part of the thesis develops two correction algorithms—one based on the ODrlt test statistic and the other on LASSO goodness of fit—which operate within a multi-stage correction scheme guided by potential functions to iteratively refine group membership and correct MMEs.