Pursuing a PhD in theoretical physics, Andrea Montanari pursued his passion of understanding how things work at a fundamental level. Today, his research aims to understand patterns in complex, high-dimensional data. He also helps students find pleasure in figuring out something new, or creating something from scratch!
What made you decide to be a professor, and what made you want to be at Stanford?
I guess mine is an atypical background. I did my PhD in physics, more precisely theoretical physics. I was (and still am) passionate about understanding how things work at a fundamental level. If you want to pursue this passion, there is no better place than academia.
How did you choose your field of research?
During my PhD, my focus was largely on statistical physics. This area of physics aims at explaining macroscopic patterns (e.g., why water freezes when you cool it) in terms of interactions between microscopic
components (atoms, molecules, etc.).
Nowadays I am more interested in understanding patterns in complex high-dimensional data, and what are the mathematical and algorithmic methods that can be used to disentangle them from noise.
Who has influenced your work and why.
Really too many people to name (mentors, collaborators, etc.). I was lucky to be able to wander across discipline boundaries and I always found fantastic collaborators that I learnt a lot from. I prefer not to put down a list, it would be too long, but anybody can figure it out from my co-authors.
Briefly explain a project you are currently working on.
Recently I have been very interested in network and matrix data. Many modern datasets take this form (social network, recommendation systems, hyperlink networks, and so on). However, even under simple assumptions, we do not know what are optimal algorithms to process these data. For instance, we might want to find an atypically dense subset of nodes in the network. This basic task is relevant for community detection, anomaly identification, clustering, dimensionality reduction, and many other applications. Despite this, we do not know of good algorithms for performing it, even after making a lot of simplifying assumptions. Even worse, we do not know what we are shooting for, i.e., how well we can hope to perform the task.
What advice do you have for new EE students?
Stanford's EE students are all very talented. However what they might not realize is that their most precious asset is to take pleasure in what they do. They should not forget the sheer fun of figuring out something new, or building something from scratch.