Work

Information-Theoretic Thresholds for Planted Dense Cycles

Year: 2024

Type: article

Abstract: We study a random graph model for small-world networks which are ubiquitous in social and biological sciences. In this model, a dense cycle of expected bandwidth$n \tau $, representing the hidden one-dimensional geometry of vertices, is planted in an ambient random graph on n vertices. For both detection and recovery of the planted dense cycle, we characterize the information-theoretic thresholds in terms of n,$\tau $, and an edge-wise signal-to-noise ratio$\lambda $. In particular, the information-theoretic thresholds differ from the computational thresholds established in a recent work for low-degree polynomial algorithms, thereby justifying the existence of statistical-to-computational gaps for this problem.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2024.3521305

Authors: Cheng Mao, Alexander S. Wein, Shenduo Zhang

Institutions: Georgia Institute of Technology, University of California, Davis

Language: English

Topic: Complex Network Analysis Techniques

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, Division of Mathematical Sciences

Awards: G1567986156, Learning Combinatorial Non-Convex Structures in Data: Statistical Foundations and Computational Methods, G3467263316, G737753268, Nonparametric Methodology for Learning from People: Inference, Algorithms, and Optimality