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Efficient gradient computation for dynamical models
B Sengupta1, K J Friston1, W D Penny1
1Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK.
Neuroimage
|April 29, 2014
Summary
This study compares gradient estimation techniques for neuroscience data assimilation. The adjoint method is most efficient for optimizing dynamical systems, especially with many parameters.
Area of Science:
- Neuroscience
- Computational Neuroscience
- Systems Neuroscience
Background:
- Data assimilation is crucial in neuroscience, from single neurons to fMRI.
- It involves inverting generative models to explain and predict data.
- Optimization typically uses gradient-based methods to extremize functionals.
Purpose of the Study:
- Compare three gradient estimation techniques for time-dependent functionals.
- Evaluate finite differences, forward sensitivities, and the adjoint method.
- Determine the most efficient method for dynamical systems.
Main Methods:
- Implemented and compared finite differences, forward sensitivities, and adjoint methods.
- Analyzed computational efficiency based on system states and parameters.
- Focused on gradient estimation for dynamical systems.
Main Results:
- The adjoint method offers the most efficient gradient computation for dynamical systems.
- This efficiency is pronounced in systems with more parameters than states.
- Forward sensitivities are computationally expensive; finite differences are intermediate.
Conclusions:
- The adjoint method is superior for optimizing complex dynamical models in neuroscience.
- Adjoint-based inversion of dynamical causal models (DCMs) can scale to large neuroimaging models.
- This facilitates the study of large-scale neural interactions and network dynamics.
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