Networks: Estimation in Protein Molecules, Modeling of Transactional Data, and Application to Ensemble Learning

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I will continue to explore a few exciting problems about networks, which I started to investigate with my previous NSERC Discovery Accelerator Supplement grant. ******First, I will work on network estimation in protein molecules. A protein molecule is made up of a sequence of amino acid residues. With a student and a colleague, I have started to study various computational problems about characterizing the 3D structures of protein molecules, one of which is the quantification of direct-coupling strengths between any two residues. This type of analysis often results in a residue-residue network, in which each node corresponds to a residue, and an edge is drawn between two nodes if their direct-coupling strength is high. This is important for the study of allostery, the process by which conformational changes at one residue site affect the conformation of another. In dealing with this problem, we have pioneered a new analytic paradigm, which will allow us to do many interesting things in statistics. ******Next, I will work on network modeling of transactional data. Network data analysis is an emerging area of statistics. Often, each node in a network can belong to one of many different communities. Researchers have used a so-called stochastic block model (SBM) to detect these communities. Early works often do not account for time and treat the network as if it were static. Recently, researchers have started to consider network dynamics over time, but they often treat the time variable in a discrete manner. With a student and a collaborator, I have been studying a continuous-time extension of the SBM, which can be used to model transactional data, e.g., messages sent over a period of time among many individuals, but I would like to further extend our model to incorporate spatial information. The resulting spatial-temporal SBM can be used to study any collection of entities that communicate with each other while travelling over space and time; it can be very useful for many branches of science.******Finally, I will apply ideas from network analysis to ensemble learning. As far as I am aware, Zhu & Chipman (2006, Technometrics 48:491-502) were the first ones to use the ensemble approach for variable selection (as opposed to prediction). Since then, I have continued to work on this problem and further crystallized the notion of variable-selection ensembles, but an open question is what constitutes a good generating mechanism. Interestingly, a student and I have discovered a new mechanism based on network analysis. So far, this new mechanism has shown outstanding performance in almost all the simulation settings we have previously considered. I am intrigued by this new discovery, and want to dig much deeper into it.******Trainees participating in this research program will be able to cultivate computational skills that are much needed in today's economy, and acquire a taste of some very challenging problems in science and engineering.