Scaled matrix completion and cell deconvolution with NanoString data

Abstract

This thesis explores two research problems in Chapters 1 and 2. Chapter 1 combines pivotal penalized estimation, with matrix completion, to introduce a new matrix completion problem, where the optimal tuning parameter does not depend on the variance of the noise. We consider this new "scaled matrix completion" problem, and compare it to standard matrix completion problem. Chapter 2 develops a new cell deconvolution method for data from NanoString Technologies nCounter platform, a relatively new sequencing platform. We assess the performance of this cell deconvolution method with simulated data and experimental data.