I've repeatedly reinvented my research interests, so I must begin with a brief history.
I started under the great Sergey Denisov in approximation theory, especially orthogonal polynomials. We generally applied techniques related to harmonic analysis (e.g. Steepest descent methods for Riemann-Hilbert problems, commutator estimates for singular integral operators, and classical martingale and probability theory as practiced in randomized Fourier analysis). My first three papers were in this area, and much more could be written with the work we did; my dissertation can be found here, though I would advise against reading it; Andreas Seeger once told me to never read your dissertation after you've defended it, advice I have followed to the letter.
I left pure mathematics with the idea of getting into machine learning; I felt I needed experience solving real problems in software in order to hone my skills in this field. I wanted to avoid the issue I felt I would encounter in academia; siloing and pigeonholing, as well as never being incentivized to create truly lean systems. For that reason I took a job with the Milwaukee Brewers Baseball Club, as their first data scientist on the business side.
With my team there, we have built systems I am very proud of, and helped lead a technology transition towards in-house software development and maintenance. The future at MBBC is bright.
In October 2018 I moved to Seattle to work on the federated learning team--work designed to allow users' data to remain on their devices while enabling massively distributed machine learning systems to actually be deployed and function in the real world.
|Pure Mathematics in Machine Learning||The insights of pure mathematics have at times been leveraged to great advantage in machine learning; see Wasserstein GAN. There are many opportunities to recast machine learning developments in mathematical terms and utilize this framing to enable better systems in practice. I consider the intersection of harmonic analysis and machine learning to be a particularly fruitful area.|
|Automatic Topology Learning||Many of the important advances in machine learning have been fundamentally topological in nature. That is, the topology of the data informs the architecture chosen. However, there has been a human in this process all along the way. As we look towards extending machine learning into new domains, how can we remove this human?|