Variational free energy and the Laplace approximation

Friston, Karl J.; Mattout, Jérémie; Trujillo-Barreto, Nelson J.; Ashburner, John; Penny, Will D.

doi:10.1016/j.neuroimage.2006.08.035

Cited by 824 publications

(869 citation statements)

References 38 publications

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“…In this context, the objective function is the (log) marginal likelihood as approximated by variational free energy. This accounts for the accuracy but also the complexity of the model of temporal correlations (Friston et al, 2007). The free energy provides a lower bound on the model evidence enabling Bayesian model comparison.…”

Section: Methodsmentioning

confidence: 99%

Accurate modeling of temporal correlations in rapidly sampled fMRI time series

Corbin

Todd

Friston

et al. 2018

Human Brain Mapping

104

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Rapid imaging techniques are increasingly used in functional MRI studies because they allow a greater number of samples to be acquired per unit time, thereby increasing statistical power. However, temporal correlations limit the increase in functional sensitivity and must be accurately accounted for to control the false‐positive rate. A common approach to accounting for temporal correlations is to whiten the data prior to estimating fMRI model parameters. Models of white noise plus a first‐order autoregressive process have proven sufficient for conventional imaging studies, but more elaborate models are required for rapidly sampled data. Here we show that when the “FAST” model implemented in SPM is used with a well‐controlled number of parameters, it can successfully prewhiten 80% of grey matter voxels even with volume repetition times as short as 0.35 s. We further show that the temporal signal‐to‐noise ratio (tSNR), which has conventionally been used to assess the relative functional sensitivity of competing imaging approaches, can be augmented to account for the temporal correlations in the time series. This amounts to computing the t‐score testing for the mean signal. We show in a visual perception task that unlike the tSNR weighted by the number of samples, the t‐score measure is directly related to the t‐score testing for activation when the temporal correlations are correctly modeled. This score affords a more accurate means of evaluating the functional sensitivity of different data acquisition options.

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Section: Methodsmentioning

confidence: 99%

Accurate modeling of temporal correlations in rapidly sampled fMRI time series

Corbin

Todd

Friston

et al. 2018

Human Brain Mapping

104

View full text Add to dashboard Cite

show abstract

“…A standard variational (Laplace) Bayesian scheme was used to approximate the conditional density over parameters by maximizing a negative free energy bound on log-model evidence (Friston et al, 2007). This inversion was used to assess which models (1-10) best explained the theta and gamma changes.…”

Section: Bayesian Model Inversion and Selectionmentioning

confidence: 99%

Losing Control Under Ketamine: Suppressed Cortico-Hippocampal Drive Following Acute Ketamine in Rats

Moran

Jones

Blockeel

et al. 2014

Neuropsychopharmacol

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Systemic doses of the psychotomimetic ketamine alter the spectral characteristics of hippocampal and prefrontal cortical network activity. Using dynamic causal modeling (DCM) of cross-spectral densities, we quantify the putative synaptic mechanisms underlying ketamine effects in terms of changes in directed, effective connectivity between dorsal hippocampus and medial prefrontal (dCA1-mPFC) cortex of freely moving rats. We parameterize dose-dependent changes in spectral signatures of dCA1-mPFC local field potential recordings, using neural mass models of glutamatergic and GABAergic circuits. Optimizing DCMs of theta and gamma frequency range responses, model comparisons suggest that both enhanced gamma and depressed theta power result from a reduction in top-down connectivity from mPFC to the hippocampus, mediated by postsynaptic NMDA receptors (NMDARs). This is accompanied by an alteration in the bottom-up pathway from dCA1 to mPFC, which exhibits a distinct asymmetry: here, feed-forward drive at AMPA receptors increases in the presence of decreased NMDAR-mediated inputs. Setting these findings in the context of predictive coding suggests that NMDAR antagonism by ketamine in recurrent hierarchical networks may result in the failure of top-down connections from higher cortical regions to signal predictions to lower regions in the hierarchy, which consequently fail to respond consistently to errors. Given that NMDAR dysfunction has a central role in pathophysiological theories of schizophrenia and that theta and gamma rhythm abnormalities are evident in schizophrenic patients, the approach followed here may furnish a framework for the study of aberrant hierarchical message passing (of prediction errors) in schizophrenia-and the false perceptual inferences that ensue.

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“…Here, we revisit questions about the generation of distributed responses by analysing the data using conventional deterministic DCMs (EM), stochastic DCMs under the mean-field approximation (DEM) and generalised filtering (GF). The mathematical details of these schemes are described in a series of technical papers (e.g., EM: Friston et al, 2007;DEM: Friston et al, 2008;GF: Friston et al, 2010). In this paper, we focus on the products of these schemes and how they differ from each other.…”

Section: Stochastic Dcmmentioning

confidence: 99%