Statistics and Probability seminar
Speaker: Sagnik Nandy, The Ohio State University, Columbus
Host: Koushik Saha
Title: Degree-Heterogeneous Networks: Optimality, Inference, and Privacy
Time, day and date:  10:00:00 AM – 11:00:00 AM, Tuesday, March 10
Venue: https://meet.google.com/wjs-deag-ysh Online
Abstract: Networks arising in real relational datasets exhibit strong degree heterogeneity: the propensity of nodes to participate in interactions varies widely. When the full set of edges is unavailable or too sensitive to release, degree summaries often become the primary data object, motivating the classical $\beta$-model and its higher-order extension to hypergraphs. In this talk, I develop a statistical theory for degree-heterogeneous $r$-uniform hypergraphs using the hypergraph $\beta$-model. First, I characterize sharp estimation rates for the maximum likelihood estimator (MLE) of the model parameters in both $\ell_2$ and $\ell_\infty$ losses, highlighting an effective sample size scaling of order $n^{r-1}$ per node parameter. I then prove that these rates are minimax optimal. Next, I study inference where I characterize minimax detection thresholds for testing the presence of degree heterogeneity.
Finally, I turn to privacy. Using edge differential privacy, I quantify the statistical price of privacy for estimation in $\beta$ models and show a sharp separation between local and central privacy regimes. Simulations illustrate the predicted privacy–utility tradeoffs, and an application to the Enron email hypergraph demonstrates the impact of different regimes of privacy on link prediction in a real organizational communication network.
(Work based on joint papers with B. Bhattacharya and B. Mandal.)