Overview
Talk Title: Testing model/data fit for networks arising in biological contexts
Abstract:
Data in the form of graphs are common in many biological contexts. In systems biology, graphs are used to record protein-protein interactions. In neuroscience, graphs are used to record synaptic contacts between neurons. Both protein-protein interaction networks and neuronal networks have been used as examples of scale-free networks, that is, networks whose degree distribution follows a power law. Descriptive statistics have been used to study these networks, suggesting a degree-based edge formation mechanisms in these data. However, both of these networks have yet to be rigorously analyzed using a model-fitting approach. Part of the difficulty in studying such networks within a model-based setting is that statistical theory regarding fitting random graph models is still in development, since it poses several challenging combinatorial and algorithmic problems.
This talk will discuss the problem of model/data fit in the context of these two biological examples, and the recent work in solving this problem for data in the form of a graph. The methods we use come from algebraic statistics and graph theory. We will explain briefly the mathematics behind the testing algorithm, and demonstrate how the method is used on two data sets from biology: the connectome of C. elegans and the interactome tof Arabidopsis thaliana. These two networks have been popular examples in the network science literature. Our work provides a model-based approach to studying them.
Sonja Petrović is a Professor of Applied Mathematics at the Illinois Institute of Technology. Petrović’s research is in nonlinear algebra and nonlinear statistics. Petrović develops, analyzes, and applies statistical models for discrete relational data such as networks. Petrović also studies randomized algorithmic approaches to computational algebra problems whose expected runtimes are much lower than the well-known worst-case complexity bounds, develop probabilistic models to study average and extreme behavior of algebraic objects, and use machine learning to predict and improve the behavior of algebraic computation.
Learn more about Sonja Petrović’s research
The NSF-Simons National Institute for Theory and Mathematics in Biology Seminar Series aims to bring together a mix of mathematicians and biologists to foster discussion and collaboration between the two fields. The seminar series will take place on Fridays from 10am – 11am at the NITMB offices in the John Hancock Center in downtown Chicago. There will be both an in-person and virtual component.