Speaker: Samson Zhou
Affiliation: Carnegie Mellon University

Title: Tight Bounds for Adversarially Robust Streams and Sliding Windows via Difference Estimators

Abstract:
We introduce difference estimators for data stream computation, which provide approximations to F(v)-F(u) for frequency vectors v,u and a given function F. We show how to use such estimators to carefully trade error for memory in an iterative manner. The function F is generally non-linear, and we give the first difference estimators for the frequency moments F_p for p between 0 and 2, as well as for integers p>2. Using these, we resolve a number of central open questions in adversarial robust streaming and sliding window models.

For both models, we obtain algorithms for norm estimation whose dependence on epsilon is 1/epsilon^2, which shows, up to logarithmic factors, that there is no overhead over the standard insertion-only data stream model for these problems.

Speaker: Zeyu Guo
Affiliation: Ohio State University

Title: TBD

Abstract: TBD

Speaker: Yuzhou Gu

Affiliation:NYU Center for Data Science & Courant Institute

Title: Community detection in the hypergraph stochastic block model

Abstract:

Community detection is a fundamental problem in network
science, and its theoretical study has received significant attention
over the last decade. In this talk I will present some recent advances
on the community detection problem in sparse hypergraphs. In
particular, we determine the weak recovery threshold for the
hypergraph stochastic block model for a wide range of parameters. This
resolves conjectures made by physicists in the corresponding regimes
and has implications to phase transitions of random constraint
satisfaction problems. A key component in this study is to analyze the
behavior of information channels under repeated applications of the
belief propagation operator. We introduce a framework for performing
this analysis based on information-theoretical methods for channel
comparison. Along the way, we formulate a rigorous version of the
population dynamics algorithm, an approach commonly used in practice
but lacks theoretical guarantees.