Learning Sparse Graphons and the Generalized Kesten-Stigum Threshold
This addresses a bottleneck in graphon learning for sparse, homogeneous graphs, offering a solution for researchers in network analysis and machine learning.
The paper tackles the problem of learning graphons in the constant expected degree regime, providing an efficient algorithm that succeeds in estimating the rank-k projection of a graphon in the L2 metric under a generalized Kesten-Stigum condition.
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in order to succeed with efficient algorithms in the challenging cases where the local structure of the graph is homogeneous. This paper provides an efficient algorithm to learn graphons in the constant expected degree regime. The algorithm is shown to succeed in estimating the rank-$k$ projection of a graphon in the $L_2$ metric if the top $k$ eigenvalues of the graphon satisfy a generalized Kesten-Stigum condition.