The NSF-Simons National Institute for Theory and Mathematics in Biology is bringing together mathematicians and biologists each week for the NITMB Seminar Series. NITMB Seminar Series talks cover diverse topics and are given by either visiting researchers or NITMB members. These talks take place in-person at the NITMB Collaboration Hub in downtown Chicago, with a webinar available for remote attendees. We are proud to invite a wide variety of scientists and mathematicians to mingle and explore topics of interest for the convergence of mathematics and biology. One speaker presenting as part of the NITMB Seminar Series is Sonja Petrović.
Sonja Petrović, Professor, Applied Mathematics, Illinois Institute of Technology
Sonja Petrović is a Professor of Applied Mathematics in the College of Computing at the Illinois Institute of Technology. Petrović’s research is in nonlinear algebra and nonlinear statistics. She develops, analyzes, and applies statistical models for discrete relational data such as networks.
Petrović also studies randomized algorithm approaches to computational algebra problems whose expected runtimes are much lower than the well-known worst-case complexity bounds, develops probabilistic models to study average and extreme behavior of algebraic objects, and uses machine learning to predict and improve the behavior of algebraic computations.
We spoke with Sonja Petrović to explore her work with statistical models and the applications these models could have in biological research.
What is a big question you’ve been asking throughout your research?
“There are several questions that have motivated much of my work, but they are centered around the following core problem: how to reliably test whether a statistical model fits the observed data. This question should be posed and answered before parameter estimation, which is known as model fitting in some areas, and interpreting the results from the fitted models. When I say 'model', I mean a statistical model, represented as a family of probability distributions of a given form. Model fitting the data means that the model provides a plausible explanation for how the data was generated, that is, there exists a value of the parameters that explain the data fairly well. If the model form does not fit well, then all of the interpretations are pointless, since the context for estimation and evaluation is incorrect in the first place. The difficulty of answering this question for highly structured, high dimensional, and sparse data is exactly what drives most of what I do.”
What disciplines does your research integrate?
“I work in computational mathematics and mathematical statistics. Specifically, on the statistics side, I work in algebraic statistics and statistical modeling of relational data such as networks. There are many areas of applications, such as biology, social sciences, and economics. On the mathematics side, my work is in nonlinear algebra: randomized algorithm approaches to computational algebra. I use probabilistic methods, and I use machine learning to predict and improve some algebraic computations.”
Where do you find inspiration?
“My inspiration to keep going comes from the people I work with, the city of Chicago and my travels, and seeing the family’s curiosity about the world. In fact, when you see kids asking the right –difficult and open-ended– questions, you realize we should all be asking these questions. If somewhere in the education process we lose our curiosity, then the world isn’t working the way it ought to. I get mostly inspired by basic ‘but why?’ questions.
On the professional side, inspiration for the problems I want to work on comes from applied research with social impact. For me, at the moment, this comes from social sciences and economics. Since my last year of graduate school, I have also been motivated by the work of late Stephen Feinberg. He took me under his wing as a mentor when we had a joint research project. Everything he has written continues to provide endless inspiration. I also find inspiration in students and postdocs. In research it can be easy to forget the humans involved, but it’s really humans and our relationships and joint discovery that drive all innovation.”
What aspects of your research could be interesting to mathematicians or applied to biology?
“The question 'does the model fit the data' is such a fundamental one, yet it has been tackled in biology only relatively recently. And in fact, this is the topic of my talk at NITMB. I will talk about one particular example: network modeling, taking a couple of data sets that come from biology and explaining the impact of this question. Biology is complex. The novel and exciting data sets are ever changing in structure and type, and as the science itself grows, modeling questions grow with it. And I think we – statisticians and mathematicians – are still catching up with the correct mathematical tools to evaluate which models would be best to use. That’s where the question of model fit comes in beautifully to help us interpret the computational results.”
What about the NITMB do you find exciting?
“I think connections between math and biology are extremely difficult to make by oneself. Having an institute such as this one offer to host a dialogue between mathematicians and biologists, where I can be there and answer questions from the biology side and ask questions to the biology side, and people are interested in trying to help me learn, is important. Oftentimes in interdisciplinary dialogues, translation is 80% of the work. And so the value that I think the Institute will bring to people like me is this opportunity to ask questions and to learn how best to translate what I’m doing to biology.”
What career achievement are you most proud of?
“Seeing opportunities where I am told none exist! I came from a small European country to study in the United States. The immigrant life is not easy, and we all know it; I am sure when I say I was told ‘no’ to almost every initiative I wanted to take, many immigrants will feel seen. For example, I was told that I: can’t get a scholarship to go to college, but I did; can’t go to a research institution and get a PhD, but I did; can’t get a research postdoc, but I did; and so on. At the other end of this journey, I’m most proud of being able to support my research group through external grants over the years. My first student, when she graduated, obtained an NSF postdoc and a tenure track position at the same time, and she’s now tenured with an NSF career grant under her belt. So just seeing where my former students go, whether academia or industry, that makes me more proud than other things.”
Outside of your research, what other interests do you have?
“I love to travel! I think traveling is probably my reason for living. I love biking. I’m a proud card carrying member of Active Transportation Alliance. I’m a local school bike bus organizer, meaning I gather a bunch of people and protect kids on the road as they bike to elementary school once a week, and I try to rally support from the community. I’m really interested in music; I was a musician once in my life. If there’s a live music show I can go to, I’ll probably go. I’m into dancing of almost any kind. And I really want to learn Spanish.”
What are you hoping to work on in the future?
“There are two things. One, I really want to work on economic and social networks because there’s so much data out there, even in the city of Chicago itself. There’s data that is relevant, and there are people working on problems, and I would love to join them and help solve their applied problems using the tools that we’re developing. The second thing is: more biology, please! I want to know how to better incorporate the theory and model-based approaches to this data analysis motivated by the lab. I’m hoping one of the outcomes of my talk will be to make more connections. In my department, we recently hired new faculty members who work in related areas. But I’m also looking to connect outside to people who don’t do math so I can learn their applied problems and figure out how to translate those to mathematical formulation.”
More information about Petrović’s work is also available in Petrović’s recent publications: