On the Finite-Sample Complexity of System Identification in Temporally Homogeneous Discrete-Time Fractional-Order Dynamical Systems.
Sarthak Chatterjee, Sérgio Pequito · arXiv (Cornell University) · 2021
Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as electroencephalogram (EEG) and electrocorticogram (ECoG). Although estimating the spatiotemporal parameters of DT-FODS is not a new problem, when dealing with neurophysiological signals we need to guarantee performance standards. Therefore, we need to understand the trade-offs between sample complexity and estimation accuracy of the system parameters. Simply speaking, we need to address the question of how many measurements we need to collect to identify the system parameters up to an uncertainty level. In this paper, we address this problem under the assumption that long-term memory dependencies at the state variables level do not change over time. The main result is the first result on non-asymptotic sample complexity guarantees of identifying DT-FODS. Finally, we provide evidence of the efficacy of our method in the context of forecasting real-life EEG time series.