Research
My broad goal is to use methods from statistical physics and (quantum and classical) information theory to gain insight into complex systems like networks. Below are a few active research directions.
* Information theoretic approaches to understand the relationship between structure and function in networks. In particular, how can we use activity on the network to identify the most important network features? We use a notion called information transfer, or transfer entropy, to accomplish this. Of course, estimating this quantity with limited data is tricky.
* Many papers have differentiated influence and homophily on social networks, but Shalizi and Thomas have pointed out that latent homophily can not be distinguished from influence. I am exploring the conditions under which latent homophily can be ruled out as an explanation for correlations. More generally, I would like to extend the notion in quantum physics of a test for hidden variables (the Bell inequalities, e.g.) to various hidden variable models in machine learning contexts (latent homophily being only one example). This differs from the typical computer science approaches. For instance, hypothesis testing generally considers a null hypothesis, an alternate hypothesis, and the relative likelihood. We take a hidden variable model as the null hypothesis and construct a test to rule it out altogether. The other approach taken is to assume hidden variables exist and then use some learning algorithm to find their most likely values. This approach gives you an answer but it doesn't tell you if you asked the wrong question! With Aram Galstyan.
* Mapping graph clustering to an Ising problem gives us a framework for asking several questions. When are clusters detectable? Is clustering always stable? Which prior information would affect these properties? With Aram Galstyan and Armen Allahverdyan.
* A new generation of quantum chips made by D-wave solve Ising problems using a quantum annealing process. Our work on clusters shows that not all Ising problems are created equal: there is a rich phase structure. How does this structure affect the quality of solutions achievable through quantum annealing?
* Modelling dynamic networks. We would like to understand the co-evolution of links and attributes on dynamic networks. With Yoon Sik Cho and Aram Galstyan.
Teaching
I'm currently co-teaching CS 599, "Computation and physics" with Aram Galstyan.