期刊
IEEE ACCESS
卷 8, 期 -, 页码 196865-196877出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/ACCESS.2020.3034077
关键词
Noise measurement; Optimization; Smoothing methods; Correlation; Biological system modeling; Sensors; Numerical differentiation; derivatives; optimization; data-driven modeling
资金
- Moore/Sloan Data Science
- Washington Research Foundation Innovation in Data Science Postdoctoral Fellowship
- Sackler Scholarship in Biophysics
- National Institute of General Medical Sciences of the National Institutes of Health [P20GM103650]
- Air Force Office of Scientific Research [FA9550-19-1-0011, FA9550-19-1-0386]
- Washington Research Foundation
- National Institute of Health [1R01MH117777]
Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or designing control. Unfortunately, the mathematical formulation of numerical differentiation is typically ill-posed, and researchers often resort to an ad hoc process for choosing one of many computational methods and its parameters. In this work, we take a principled approach and propose a multi-objective optimization framework for choosing parameters that minimize a loss function to balance the faithfulness and smoothness of the derivative estimate. Our framework has three significant advantages. First, the task of selecting multiple parameters is reduced to choosing a single hyper-parameter. Second, where ground-truth data is unknown, we provide a heuristic for selecting this hyper-parameter based on the power spectrum and temporal resolution of the data. Third, the optimal value of the hyper-parameter is consistent across different differentiation methods, thus our approach unifies vastly different numerical differentiation methods and facilitates unbiased comparison of their results. Finally, we provide an extensive open-source Python library pynumdiff to facilitate easy application to diverse datasets (https://github.com/florisvb/PyNumDiff).
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