Efficient PAC Learnability of Dynamical Systems Over Multilayer Networks
This work addresses the challenge of modeling cascading phenomena like disease spread in multilayer networks, providing theoretical foundations for future research, but it is incremental as it extends prior single-layer methods to a more complex setting.
The paper tackles the problem of learning dynamical systems over multilayer networks, which are more realistic than single-layer models, and presents an efficient PAC learning algorithm with provable guarantees, showing that only a small number of training examples is needed, along with a tight analysis of the Natarajan dimension for model complexity.
Networked dynamical systems are widely used as formal models of real-world cascading phenomena, such as the spread of diseases and information. Prior research has addressed the problem of learning the behavior of an unknown dynamical system when the underlying network has a single layer. In this work, we study the learnability of dynamical systems over multilayer networks, which are more realistic and challenging. First, we present an efficient PAC learning algorithm with provable guarantees to show that the learner only requires a small number of training examples to infer an unknown system. We further provide a tight analysis of the Natarajan dimension which measures the model complexity. Asymptotically, our bound on the Nararajan dimension is tight for almost all multilayer graphs. The techniques and insights from our work provide the theoretical foundations for future investigations of learning problems for multilayer dynamical systems.