Two Sigma Fellowships recognize doctoral students pushing the frontiers of STEM fields such as applied mathematics, computer science, physics, and statistics. In our series, The Fellowship Forum, we catch up with past and present Two Sigma Fellows to spotlight the fascinating research they’re pursuing in their respective fields.
Spencer Compton is a Two Sigma Fellow and doctoral student at Stanford University. We spoke with Spencer about how the Two Sigma Fellowship has supported his doctoral journey and his work on designing algorithms for statistical problems at the intersection of theoretical computer science and information theory.
What is your area of research, and what excites you the most about your field?
Most of my research is about designing algorithms for statistical problems, with an eye towards using techniques from theoretical computer science and information theory. There is a surprising amount that we don’t know about this area — even for tasks as basic as learning distributions from a limited number of samples, performing linear regression, or estimating the mean of a distribution.
Many of my favorite questions are inspired by how modern statistics faces new algorithmic challenges, such as how datasets are getting larger and larger, data is scraped from very distinctive sources, and algorithms are deployed in settings the designer might not have considered. These challenges motivate some pretty exciting research, like studying the design of fast algorithms, understanding the limits of how accurate or adaptive an estimator may be, and more broadly trying to understand what structure makes statistical tasks easy or hard.
What does having the fellowship behind you mean for the day-to-day reality of doing your research?
I’m very grateful for Two Sigma’s support. I have a bunch of research problems that I am very excited about, and it is so helpful to have the funding to work on the research I love.
What’s happening in your field right now that you think deserves more attention?
When I talk to people in other fields, I think something they find surprising is how many fundamental results in algorithmic statistics were only proven very recently. Some amazing lines of work in the past couple of decades have charted a fascinating algorithmic landscape yielding the first efficient algorithms for many core problems in high-dimensional statistics.
What’s something about your doctorate journey that has surprised you?
Something I didn’t comprehend at first is how research is an ecosystem of sorts. Within a subfield, you really can see how our understanding of the core underpinnings evolves over time. I think it’s very fun to follow along as the community pushes the frontier and develops new insights; to me, this perspective really motivates framing your own insights in a way that might contribute a bit back to this ecosystem.
What advice would you give someone starting a doctorate?
Everyone says to choose a great advisor, and they are 100% correct; I am very lucky in this regard to have two fantastic advisors in Tselil Schramm and Gregory Valiant. Even with the best advisors, a lot of the PhD journey is very self-motivated, so I think it is important to work on the problems you personally find the most compelling. I do my best work when I am thinking about problems that I am extremely curious about the answer to, where I would excitedly read the paper if I woke up one morning and someone else had solved it.
What’s a question or idea outside your core research that you can’t stop thinking about?
I think it’s really intriguing how many decisions in the world are algorithmic problems. For example, any time you order a car on a rideshare app, there is a rich space of ways you could match riders and drivers. It’s interesting to see how these sorts of decisions end up being made in practice, and to daydream a bit about how else they could be done.
Is there something you’re passionate about beyond your research that influences how you approach your work?
I find it fun when you can think of a neat way of explaining an unintuitive concept — whether it’s in research, teaching, or just a conversation. Outside of work I’m passionate about pizza and bad puns, but I doughn’t think they help me professionally.