The paper Bayesian hierarchical dictionary learning coauthored by Nathan Waniorek, Daniela calvetti and Erkki Somersalo, has been published in the journal Inverse Problems. The paper, which grew out of Nathan’s senior capstone project, proposes to use sparsity promoting Bayesian solvers for expressing new data in terms of an existing dictionary, combining Bayesian scientific computing and mathematics of data science into a very effective sparse coding and classification tool.
Here are Nathan’s reflections on how his research experience at CWRU solidified his appreciation and interest in applied mathematics.
Doing my undergrad in Applied Math at CWRU prepared me very well for continuing on to a PhD program in Computational and Applied Mathematics. The math department at CWRU is unique in that it is a smaller department with a lot of exceptional professors that are very invested in the undergraduate program. I found that because of this environment, it was very easy to form meaningful relationships with great mentors that helped me become excited about applied mathematics and helped me be successful in pursuing a research career. My senior year, I worked with Professors Calvetti and Somersalo on my capstone project that led to this paper. The project combined ideas from two courses that I took with them the previous semester in data mining and Bayesian scientific computing. This was really the first time I was able to see how the math I had learned in my classes could be used in new ways to solve important problems. Working on this project was an invaluable experience and it solidified my interest in pursuing a career in mathematics research.
I am currently at the University of Chicago pursuing my PhD in Computational and Applied Mathematics. My research is still focused on Bayesian inverse problems. Currently, I am interested in analyzing the error and computational cost of discretizations of Bayesian inverse problems that are formulated in function spaces. The techniques I use are strongly informed by the courses I took at CWRU, especially the courses on Bayesian scientific computing, PDE’s, and finite-element methods.