Theory to gain insight and inform practice: re-run of IMS Rietz Lecture, 2016

Henry L. Rietz, the first president of IMS, published his book “Mathematical Statistics” in 1927. One review wrote in 1928: “Professor Rietz has developed this theory so skillfully that the ’workers in other fields’, provided only that they have a passing familiarity with the grammar of mathematics, can secure a satisfactory understanding of the points involved.” In this lecture, I would like to promote the good tradition of mathematical statistics as expressed in Rietzs book in order to gain insight and inform practice. In particular, I will recount the beginning of our theoretical study of dictionary learning (DL) as part of a multi-disciplinary project to “map a cell’s destiny” in Drosophila embryo. I will share insights gained regarding local identifiability of primal and dual formulations of DL. Furthermore, comparing the two formulations is leading us down the path of seeking confidence measures of the learned dictionary elements (corresponding to biologically meaningful regions in Drosophila embryo). Finally, I will present preliminary work using our confidence measures to identify potential knockout (or gene editing) experiments in an iterative interaction between biological and data sciences.