Dr. Liza Levina joined the Department of Statistics at the University of Michigan in 2002 after receiving her Ph.D. in Statistics from UC Berkeley. Today, she is the Vijay Nair Collegiate Professor of Statistics and affiliated faculty at the Michigan Institute for Data Science (MIDAS) and the Center for the Study of Complex Systems. She also serves as the Ph.D. Program Director and Associate Chair of Statistics. 

Liza studied mathematics as an undergraduate but switched to statistics for her Ph.D. because she wanted to have a closer connection to the real world. Her current research interests focus on statistical analysis of network data and its applications, from social media to neuroimaging. One challenge of networks is that we can no longer rely on an independent identically distributed sample: network data is about connections between nodes, which are not independent, and frequently there is only one observation to work with (there is only one Facebook, not a sample of them). Computational challenges in this field require working with large sparse matrices and solving difficult optimization problems;   mathematical challenges call for tools from modern random matrix theory. Working with multiple networks, as in neuroimaging (each person has their own brain connectivity network), presents its own opportunities and challenges. On one hand, we are back to having a sample, which is good. On the other hand, how exactly do we compute the sample mean of networks, or perform a two-sample test?   Many of these very basic questions remain open for networks.

Facebook friends of one student. The intersecting communities are identified by our algorithm. (Photo by: Jesus Arroyo)

On neuroimaging applications, Liza collaborates with faculty from Psychiatry who study both abnormal brain patterns, e.g. those in schizophrenia or PTSD, and normal brain development in children and adolescents. These data are extremely noisy, but there is definitely signal: if you take resting state fMRI-based brain networks of schizophrenics and healthy controls, and throw them into your favorite off-the-shelf classifier, you’ll get 80% accuracy; with a bit more effort, you can get over 90% accuracy. But if you ask just how the schizophrenic brains differ from normal ones, it’s a much harder question to answer, and the usual variable selection tools don’t help much – features are edge weights, and there are far too many predictive edges which don’t tend to arrange themselves into a nice interpretable pattern.    Developing “network-aware” prediction and variable selection methods, which can be interpreted in terms of larger network structures and not just the individual edges, is a current key research goal in Liza’s group. 

Most Ph.D. students in the department know Liza first and foremost as the Ph.D. program director, and she finds that role extremely rewarding. As interesting as research is, it rarely has the kind of immediate and tangible impact on people’s lives as advising and mentoring sometimes do, and Liza very much enjoys interacting with students and helping them find career paths that are best for them, whatever they may be. 

Fun Fact: According to Liza’s three children, she can only cook about three things, and one of them is salad. According to Liza, this is not true, but she admits that the kids probably don’t have enough empirical data to reject this hypothesis.