Louis Cammarata received his PhD from Harvard University in 2024 in the Department of Statistics, co-advised by Professors Tracy Ke and Caroline Uhler (MIT). He was also part of the Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard. Prior to Harvard University, Louis earned his BSc from École Polytechnique, France, and his MSc in Technology & Policy from the Massachusetts Institute of Technology (MIT). He now works as a Consultant at Bain & Company in Boston. This talk will take place as part of the IMS Lawrence D Brown PhD Student Award session, at JSM Nashville, on Wednesday, August 6, at 2:00pm.

Dynamic Networks with Possibly Erratic Changes over Time

Dynamic analysis is a fundamental problem in network analysis. Real networks often exhibit a dynamic or multi-layered nature. Unlike static network analysis which relies on a single snapshot, dynamic network analysis focuses on the mechanisms driving the time evolution of network properties. For example, trade relationship between countries or gene regulatory networks are expected to change over time and cell development. Historically considered a blind spot within network science due to its complexity and limited data availability, dynamic network analysis has recently become an active area of research holding great potential for applications in the social sciences, biology, and many other disciplines.

We start by introducing the dynamic degree-corrected, mixed membership, stochastic block model. Consider a dynamic network setting where we have a total of T mixed-membership networks for the same set of n nodes and K communities. We assume that, in each snapshot, there may be severe degree heterogeneity, and across time, the degrees of a node may have erratic changes, but the memberships of the node may evolve slowly. We are interested in estimating the memberships of all n nodes across all T snapshots. The problem is complex, for we need to address multiple challenges simultaneously; and often, fixing an existing issue may introduce a new problem. We have explored several seemingly plausible approaches and found all of them to be non-optimal.

Leveraging the insights gained from these studies, we propose dyn-MSCORE as a new approach to estimating mixed memberships. Our method combines kernel smoothing with Mixed-SCORE and incorporates several new ideas, which enable us to resolve all major issues (e.g., temporal misalignment, nonlinearity, and severe degree heterogeneity) simultaneously without producing a new major issue. We establish sharp bounds for the error rates of dyn-MSCORE and demonstrate that the rates are optimal. Additionally, we identify an interesting phase transition, depicting how the error rates and optimal kernel bandwidths depend on T and network sparsity. We further investigate the benefit of kernel smoothing, identifying two sub-regions where kernel smoothing is helpful and not helpful, respectively. Our method is supported by simulated studies and real-data examples, including representing and analyzing trading patterns between countries using international trade data.

This talk is based on my PhD work with Professor Tracy Ke at Harvard University along with Professor Jiashun Jin from Carnegie Mellon University.