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Network discovery with DCM.

Friston KJ, Li B, Daunizeau J, Stephan KE - Neuroimage (2010)

Bottom Line: The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks.The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions.We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies.

View Article: PubMed Central - PubMed

Affiliation: The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, UK. k.firston@fil.ion.ucl.ac.uk

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Related in: MedlinePlus

Comparative evaluation of log evidence approximations: This figure presents a comparative evaluation of the post hoc log-evidence based upon the conditional density of the full model and the approximation based upon explicit inversions of reduced models. The free-energy of reduced models is plotted against the reduced free-energy in the upper panel and shows a reasonable agreement. The true model is shown as a red dot. The dashed line corresponds to a 100% agreement between the two approximations. The lower panel shows the same data but here as a function of graph size (number of bidirectional edges). The reduced free-energy approximation is shown in black, while the free-energy of reduced models is shown in cyan. Reassuringly, the true model has the highest log-evidence under both proxies, for the correct graph size
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f0035: Comparative evaluation of log evidence approximations: This figure presents a comparative evaluation of the post hoc log-evidence based upon the conditional density of the full model and the approximation based upon explicit inversions of reduced models. The free-energy of reduced models is plotted against the reduced free-energy in the upper panel and shows a reasonable agreement. The true model is shown as a red dot. The dashed line corresponds to a 100% agreement between the two approximations. The lower panel shows the same data but here as a function of graph size (number of bidirectional edges). The reduced free-energy approximation is shown in black, while the free-energy of reduced models is shown in cyan. Reassuringly, the true model has the highest log-evidence under both proxies, for the correct graph size

Mentions: To assess the accuracy of the free-energy bound on log-evidence, we explicitly inverted each model and recorded its free-energy. The results in Fig. 7 testify to the quality of the free-energy bound and demonstrate a reasonable correspondence between the proxy in Eq. (9) and the log-evidence as approximated with the free-energy of each reduced model. To achieve this correspondence we had to apply a model prior that penalised each connection by a fixed amount (by subtracting a log-prior cost of 45.8 per connection). Strictly speaking this should not be necessary; however, Generalised Filtering optimises a posterior over parameters that is time-dependent (i.e., optimises the time or path integral of free-energy). This complicates the relationship between posteriors on parameters (which change with time) and priors (which do not). The free-energy used here is therefore based on the Bayesian parameter average over time (see Friston et al., 2010, Appendix 2 for details). Despite this complication, it is reassuring to note that, in models with the correct size, both the post hoc and explicit log-evidence proxies identify the same and correct model (see the lower panel of Fig. 7).


Network discovery with DCM.

Friston KJ, Li B, Daunizeau J, Stephan KE - Neuroimage (2010)

Comparative evaluation of log evidence approximations: This figure presents a comparative evaluation of the post hoc log-evidence based upon the conditional density of the full model and the approximation based upon explicit inversions of reduced models. The free-energy of reduced models is plotted against the reduced free-energy in the upper panel and shows a reasonable agreement. The true model is shown as a red dot. The dashed line corresponds to a 100% agreement between the two approximations. The lower panel shows the same data but here as a function of graph size (number of bidirectional edges). The reduced free-energy approximation is shown in black, while the free-energy of reduced models is shown in cyan. Reassuringly, the true model has the highest log-evidence under both proxies, for the correct graph size
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3094760&req=5

f0035: Comparative evaluation of log evidence approximations: This figure presents a comparative evaluation of the post hoc log-evidence based upon the conditional density of the full model and the approximation based upon explicit inversions of reduced models. The free-energy of reduced models is plotted against the reduced free-energy in the upper panel and shows a reasonable agreement. The true model is shown as a red dot. The dashed line corresponds to a 100% agreement between the two approximations. The lower panel shows the same data but here as a function of graph size (number of bidirectional edges). The reduced free-energy approximation is shown in black, while the free-energy of reduced models is shown in cyan. Reassuringly, the true model has the highest log-evidence under both proxies, for the correct graph size
Mentions: To assess the accuracy of the free-energy bound on log-evidence, we explicitly inverted each model and recorded its free-energy. The results in Fig. 7 testify to the quality of the free-energy bound and demonstrate a reasonable correspondence between the proxy in Eq. (9) and the log-evidence as approximated with the free-energy of each reduced model. To achieve this correspondence we had to apply a model prior that penalised each connection by a fixed amount (by subtracting a log-prior cost of 45.8 per connection). Strictly speaking this should not be necessary; however, Generalised Filtering optimises a posterior over parameters that is time-dependent (i.e., optimises the time or path integral of free-energy). This complicates the relationship between posteriors on parameters (which change with time) and priors (which do not). The free-energy used here is therefore based on the Bayesian parameter average over time (see Friston et al., 2010, Appendix 2 for details). Despite this complication, it is reassuring to note that, in models with the correct size, both the post hoc and explicit log-evidence proxies identify the same and correct model (see the lower panel of Fig. 7).

Bottom Line: The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks.The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions.We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies.

View Article: PubMed Central - PubMed

Affiliation: The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, UK. k.firston@fil.ion.ucl.ac.uk

Show MeSH
Related in: MedlinePlus