Linear Model Regression on Time-series Data: Non-asymptotic Error Bounds and Applications
Recent advances in measurement and sensing technologies have lead to the availability of an unprecedented amount of data generated by complex physical, social, and biological systems such as turbulent flow, opinion dynamics on social networks, transportation, financial trading, and drug discovery. This so-called big data revolution has resulted in the development of efficient computational tools that utilizes the data generated by a dynamic system to reason about reduce order representations of this data, subsequently utilized for classification or prediction on the underlying model.
For a wide range of real-world systems, the underlying complex dynamics makes deriving the corresponding modelsfrom first principles difficult if not infeasible. This can be due to a range of factors from the unpredictable nature of the environment to perturbations and uncertainties in the complex systems.
Estimating the underlying dynamics A after k data snapshots using the model regression R