PAC-Learning Uniform Ergodic Communicative Networks

TL;DR

This paper investigates the learnability of networks with vertex communication under uniform ergodic graph processes, establishing theoretical limits and bounds for binary classification using novel complexity measures and probabilistic techniques.

Contribution

It introduces the structural Rademacher complexity and tail bounds for uniform convergence in the context of ergodic random graph processes, advancing theoretical understanding of network learning.

Findings

Established uniform learnability as the worst-case limit.

Introduced the structural Rademacher complexity for network analysis.

Provided high probability bounds and consistency guarantees.

Abstract

This work addressed the problem of learning a network with communication between vertices. The communication between vertices is presented in the form of perturbation on the measure. We studied the scenario where samples are drawn from a uniform ergodic Random Graph Process (RGPs for short), which provides a natural mathematical context for the problem of interest. For the binary classification problem, the result we obtained gives uniform learn-ability as the worst-case theoretical limits. We introduced the structural Rademacher complexity, which naturally fused into the VC theory to upperbound the first moment. With the martingale method and Marton's coupling, we establish the tail bound for uniform convergence and give consistency guarantee for empirical risk minimizer. The technique used in this work to obtain high probability bounds is of independent interest to other mixing processes with and without network structure.