Professor Po-Ling Loh will talk about; 'Private estimation in stochastic block models'

We study the problem of private estimation for stochastic block models, where the observation comes in the form of an undirected graph, and the goal is to partition the nodes into unknown, underlying communities. We consider a notion of differential privacy known as node differential privacy, meaning that two graphs are treated as neighbors if one can be transformed into the other by changing the edges connected to exactly one node. The goal is to develop algorithms with optimal misclassification error rates, subject to a certain level of differential privacy.

We present several algorithms based on private eigenvector extraction, private low-rank matrix estimation, and private SDP optimization. A key contribution of our work is a method for converting a procedure which is differentially private and has low statistical error on degree-bounded graphs to one that is differentially private on arbitrary graph inputs, while maintaining good accuracy (with high probability) on typical inputs. This is achieved by considering a certain smooth version of a map from the space of all undirected graphs to the space of bounded-degree graphs, which can be appropriately leveraged for privacy. We discuss the relative advantages of the algorithms we introduce and also provide some lower-bounds for the performance of any private community estimation algorithm.

This is joint work with Laurentiu Marchis, Ethan D'souza, and Tomas Flidr.