Semiblind subgraph reconstruction in Gaussian graphical models

TL;DR

This paper introduces a method for reconstructing sparse subgraphs in Gaussian graphical models when only partial and noisy external information is available, addressing challenges in social networks and sensor networks.

Contribution

It proposes a penalized likelihood framework with a convex-concave iterative algorithm for semiblind subgraph reconstruction in GGMs, handling external noise and partial observations.

Findings

Effective subgraph estimation in noisy, partial data scenarios

Application to social networks and sensor networks

Improved accuracy over existing methods

Abstract

Consider a social network where only a few nodes (agents) have meaningful interactions in the sense that the conditional dependency graph over node attribute variables (behaviors) is sparse. A company that can only observe the interactions between its own customers will generally not be able to accurately estimate its customers' dependency subgraph: it is blinded to any external interactions of its customers and this blindness creates false edges in its subgraph. In this paper we address the semiblind scenario where the company has access to a noisy summary of the complementary subgraph connecting external agents, e.g., provided by a consolidator. The proposed framework applies to other applications as well, including field estimation from a network of awake and sleeping sensors and privacy-constrained information sharing over social subnetworks. We propose a penalized likelihood approach in the context of a graph signal obeying a Gaussian graphical models (GGM). We use a convex-concave iterative optimization algorithm to maximize the penalized likelihood.