Research Projects
Our group focuses heavily on interdisciplinary research, identifying and addressing mathematical problems that arise from
a variety of scientific disciplines. Below are synopsis of some major research efforts that are taking place in the group.
Interpretable Machine Learning in Microbial Ecology
Figure by Evan D. Gorman
Takeaway ...
Comparative metagenomics, a subfield of microbial ecology, aims to understand how variations in microbial populations relate to human health or environmental conditions. However, this data is very high-dimensional and noisy, rendering standard statistical techniques useless for inference. So, we have been applying signal processing and machine learning ideas to develop scientifically interpretable algorithms for comparing metagenomic samples and identifying factors (e.g., pH, water, salinity, light, etc) that differentiate them.
... Related Publications
Can one extend the above ideas beyond binary trees?
Euclidean Embeddings for Symbolic Data Science
Figure from our paper in SIAM Review
Takeaway ...
Many modern datasets are symbolic and unsuitable for traditional techniques before representing them numerically. How can one do so systematically? Much like GPS is based on tri-lateration to locate a receiver anywhere on the planet, points in possibly symbolic metric spaces can be resolved via a kind of multi-lateration. Choosing a metric that correlates with aspects relevant to classifying or regressing data, multilateration has allowed us to represent symbolic data ranging from proteins to social media posts numerically, in low-dimension, to use state-of-the-art machine learning techniques to analyze it.
Source Node Localization
Figure by Graham K. O'Connor
Takeaway ...
Many mathematical studies on infection propagation focus on the dynamics of diffusion models within a medium containing susceptible (S), infected (I), and recovered (R) entities, also known as SIR models. In comparison, far less is understood about tracing the origin of an infection source based on its space-time data. This gap in knowledge presents various theoretical and computational challenges our research group has started to pursue.