PAC-Learning Uniform Ergodic Communicative Networks
This work addresses theoretical learning limits for network communication problems, offering incremental advances in mixing processes.
The paper tackled learning networks with vertex communication under uniform ergodic random graph processes, establishing uniform learnability for binary classification and providing high-probability bounds for empirical risk minimization.
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.