Learnability of Discrete Dynamical Systems under High Classification Noise

Zirou Qiu, Zakaria Mehrab, Abhijin Adiga, Madhav Marathe, S. S. Ravi, Daniel Rosenkrantz, Richard Stearns, Anil Kumar Vullikanti

Keywords: Efficient learning under noise, Dynamical systems, PAC model, Sample complexity

TL;DR: We establish the efficient learnability of discrete dynamical systems under high classification noise

Abstract: Due to the important role of discrete dynamical systems in modeling real-world cascading phenomena on networks, problems for learning such systems have garnered considerable attention in ML. However, existing studies on this topic typically assume that the training data is noise-free, an assumption that is often impractical. In this work, we address this gap by investigating a more realistic and challenging setting: learning discrete dynamical systems from data contaminated with noise. Towards this end, we present efficient noise-tolerant learning algorithms that provide provable performance guarantees under the PAC model, and establish tight bounds on sample complexity. We show that, even in the presence of noise, the proposed learner only needs a small training set to infer a system. Notably, the number of training samples required by the algorithm in the noisy setting is the same (to within a constant factor) as the information-theoretic upper bound in the noise-free scenario. Further, the number of noisy training samples used by the algorithm is only a logarithmic factor higher than the best-known lower bound. Through experimental studies, we evaluate the empirical performance of the algorithms on both synthetic and real-world networks.

Primary Area: learning on time series and dynamical systems

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Submission Number: 7469