Limits...
Efficient gradient computation for dynamical models.

Sengupta B, Friston KJ, Penny WD - Neuroimage (2014)

Bottom Line: This is particularly true for systems where the number of parameters is greater than the number of states.For such systems, integrating several sensitivity equations - as required with forward sensitivities - proves to be most expensive, while finite-difference approximations have an intermediate efficiency.In the context of neuroimaging, adjoint based inversion of dynamical causal models (DCMs) can, in principle, enable the study of models with large numbers of nodes and parameters.

View Article: PubMed Central - PubMed

Affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK. Electronic address: b.sengupta@ucl.ac.uk.

Show MeSH
Computational efficiency for non-linear systems (A) Comparison of the gradient obtained by the three methods. Here, the last five parameters quantify the intrinsic oscillator frequencies, and the first 40 parameters the sine and cosine interaction terms. (B) Scaling of run-time as a function of the number of nodes. The absolute and relative tolerances of FD and FS methods were set to 10− 7 while the tolerances for the AM method were fixed to 10− 3. Simulation time was fixed at 100 ms.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4120812&req=5

f0020: Computational efficiency for non-linear systems (A) Comparison of the gradient obtained by the three methods. Here, the last five parameters quantify the intrinsic oscillator frequencies, and the first 40 parameters the sine and cosine interaction terms. (B) Scaling of run-time as a function of the number of nodes. The absolute and relative tolerances of FD and FS methods were set to 10− 7 while the tolerances for the AM method were fixed to 10− 3. Simulation time was fixed at 100 ms.

Mentions: The tolerance parameters of the integration process were set identical to those used for the linear models. Again, the adjoint equation being a linear first order ODE enables the use of lower tolerances (10− 3). This process was implemented for a D = 5 dimensional problem and Fig. 4(B) shows the estimated gradients.


Efficient gradient computation for dynamical models.

Sengupta B, Friston KJ, Penny WD - Neuroimage (2014)

Computational efficiency for non-linear systems (A) Comparison of the gradient obtained by the three methods. Here, the last five parameters quantify the intrinsic oscillator frequencies, and the first 40 parameters the sine and cosine interaction terms. (B) Scaling of run-time as a function of the number of nodes. The absolute and relative tolerances of FD and FS methods were set to 10− 7 while the tolerances for the AM method were fixed to 10− 3. Simulation time was fixed at 100 ms.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4120812&req=5

f0020: Computational efficiency for non-linear systems (A) Comparison of the gradient obtained by the three methods. Here, the last five parameters quantify the intrinsic oscillator frequencies, and the first 40 parameters the sine and cosine interaction terms. (B) Scaling of run-time as a function of the number of nodes. The absolute and relative tolerances of FD and FS methods were set to 10− 7 while the tolerances for the AM method were fixed to 10− 3. Simulation time was fixed at 100 ms.
Mentions: The tolerance parameters of the integration process were set identical to those used for the linear models. Again, the adjoint equation being a linear first order ODE enables the use of lower tolerances (10− 3). This process was implemented for a D = 5 dimensional problem and Fig. 4(B) shows the estimated gradients.

Bottom Line: This is particularly true for systems where the number of parameters is greater than the number of states.For such systems, integrating several sensitivity equations - as required with forward sensitivities - proves to be most expensive, while finite-difference approximations have an intermediate efficiency.In the context of neuroimaging, adjoint based inversion of dynamical causal models (DCMs) can, in principle, enable the study of models with large numbers of nodes and parameters.

View Article: PubMed Central - PubMed

Affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK. Electronic address: b.sengupta@ucl.ac.uk.

Show MeSH