The NSF-Simons National Institute for Theory and Mathematics in Biology is building community and expanding research possibilities with the Institute’s Research-In-Progress meetings. This meeting series convenes members of the NSF-Simons NITMB community to an informal venue for discussion of ongoing and planned projects. We are proud to invite a wide variety of scientists and mathematicians to share their work with our community. While Research-In-Progress meetings are only intended for members of the NITMB, we want to publicly spotlight some of the researchers who will be joining us to share insight into their career and work.
Ryan Robinett is a PhD student in the Department of Computer Science at the University of Chicago. Robinett is advised by Assistant Professor of Computer Science Lorenzo Orecchia. He is co-advised by Assistant Professor of Molecular Engineering and Medicine in the Pritzker School of Molecular Engineering Samantha J. Riesenfeld.
Ryan Robinett, PhD student in the Department of Computer Science at the University of Chicago
We spoke to Ryan Robinett to discover more about his research interests and the value the NITMB’s network and resources have provided to his career.
What is your current research area?
“My current research is at the intersection of manifold learning and Riemannian optimization, with an emphasis on applications to transcriptomics and morphology. Modern data analysis relies heavily on the Manifold Hypothesis, which states that general, empirical data distributions in Euclidean space can be closely approximated by a probability distribution over a low-dimensional manifold. Manifold learning–which I like to think of as interchangeable with the term “dimensionality reduction”–is concerned with finding a low-dimensional manifold that best represents a specific empirical distribution. Given a fixed distribution, the topological manifold best representing it is essentially unique; if you know this manifold, then you have fully characterized the state-space of the underlying system.
While learning a manifold representation in this way characterizes what observations are possible in the system, it does not fully characterize all things that can be said about the system. As an analogy: if I have learned the qualitative structure of a genetic pathway (i.e., gene A activates/suppresses gene B), there remain open questions, such as what differential equation best models gene interactions over time. Once we have a manifold structure–and especially one equipped with a Riemannian metric–we are able to perform statistical inference and machine learning on the manifold. This is the point where manifold learning ends and Riemannian optimization begins. Riemannian optimization is concerned with generalizing optimization techniques from Euclidean space to Riemannian manifolds. Riemannian notions of function gradients, shortest paths, diffusion process, etc. do not generally have closed forms, especially in the case where a manifold is learned from point cloud data. A lot of my work up to this point has been developing a numerical framework for computing these primitives quickly and accurately.”
What do you enjoy most about your research?
“I think what I find most fun about my research is that I have to switch mindsets between that of an abstract mathematician, that of a numerical methods programmer, and that of an experimentalist. In accepting the Manifold Hypothesis as truth, I have to accept that the manifolds we are trying to learn from our data can be as wily and unintuitive as Riemannian geometry and topology allow. I have to understand the abstract maths well enough so that my methods preserve the geometric and topological invariants of the underlying manifold, no matter how non-Euclidean that manifold may be. In writing software tools for other researchers, I have to creatively leverage the local Euclidean structure of Riemannian manifolds in order to make computations not prohibitively long, while taking into account the manifold curvature and homology. Lastly, I have to take myself out of the mathematical ivory tower and put myself in an experimenter’s shoes when applying my methods to real data. Just because each point in my dataset consists of n real numbers, that does not mean I can assume something like local Euclidean geometry accurately describes notions of distance. I have to take the time to understand how the data are generated and what the experimentalist is trying to capture; only then can I ascribe a local notion of distance that recapitulates known structure, which then allows my methods to be applied meaningfully.”
What excites you about the NITMB’s Research-In-Progress meetings?
“Higher-level mathematics can be difficult to comprehend, and biological systems are, in my opinion, the most difficult systems to study. At the interface of these disciplines is a lot of crying and feelings of inadequacy. Tackling problems requiring simultaneous mathematical and biological innovation takes a lot of bravery, as well as the humility to ask for help quickly and often. I am grateful for a place where this sort of transparency is welcome and where meaningful insight can be catalyzed.”
Why are you interested in the NITMB?
“While I have always felt welcome in the labs of which I have been a part, I have almost always played the role of either a mathematician or computational scientist surrounded by biologists, or as a methods researcher surrounded by optimization theorists. The NITMB has several members who straddle the same line I do. Several are trailblazers whose careers and insight give me better understanding as to how I can best leverage my unconventional position to make meaningful contributions in the long run.
Even from NITMB members who do not straddle this line, I receive valuable insight. The more conventional biologists and computationalists have helped me to better understand what are the critical application areas for manifold learning and Riemannian optimization, while those with stronger mathematical background have helped me refine my methods for difficult edge cases.”
What interests do you have outside of your research?
“In my spare time, I like learning about evolutionary biology, entropy in biological systems, and unconventional models of computation (e.g., learning about the Turing completeness of Conway’s Game of Life). In terms of leisure, I am an avid reader of science fiction, Christian theology, and history. I enjoy overpriced lattes, board game cafes, and (much to my surprise) cooking.”
What are you hoping to work on in the future?
“When I started exploring manifold learning years ago, my original motivation was to help biologists better gain insight from transcriptomic data. Single-cell RNA sequencing (scRNAseq) data is very high-dimensional (thousands to tens of thousands of genes) and infamously subject to both experimental noise and noise intrinsic to the underlying biology. For these reasons, I have had significant difficulty applying manifold learning methods to these data, despite them being my motivation. I would like help in finding problems involving transcriptomics where a manifold learning approach is comely (e.g., RNA velocity or cell state plasticity), wherein there is a meaningful notion of proximity. This could be a springboard for me to better apply my methods to transcriptomics.
While I am particularly interested in transcriptomics, I am open to general problems. Through the NITMB, I was unexpectedly presented with the opportunity to apply manifold learning to fly wing morphology. This project has been the most fun I have ever had in data analysis. Understanding the data have required careful reading of the Drosophila Morphology literature, as well as experimentation with non-Euclidean notions of distance. In addition to producing biological insight, the project has helped me refine my methods for more general application. I think the breadth of NITMB application areas–from transcriptomics to metabolism to the dynamics of evolution–there exists an inexhaustible supply of application domains and corresponding domain expertise.”
The NITMB looks forward to welcoming Ryan Robinett on Tuesday, July 23rd as part of the Research-In-Progress meeting series.