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Bayesian Estimation of Conditional Independence Graphs Improves Functional Connectivity Estimates.

Hinne M, Janssen RJ, Heskes T, van Gerven MA - PLoS Comput. Biol. (2015)

Bottom Line: A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections.As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results.The implication of this is that deterministic alternatives may misjudge connectivity results by drawing conclusions from noisy and limited data.

View Article: PubMed Central - PubMed

Affiliation: Radboud University, Institute for Computing and Information Sciences, Nijmegen, the Netherlands.

ABSTRACT
Functional connectivity concerns the correlated activity between neuronal populations in spatially segregated regions of the brain, which may be studied using functional magnetic resonance imaging (fMRI). This coupled activity is conveniently expressed using covariance, but this measure fails to distinguish between direct and indirect effects. A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections. Importantly, provided the data are normally distributed, if two variables are conditionally independent given all other variables, their respective partial correlation is zero. In this paper, we propose a probabilistic generative model that allows us to estimate functional connectivity in terms of both partial correlations and a graph representing conditional independencies. Simulation results show that this methodology is able to outperform the graphical LASSO, which is the de facto standard for estimating partial correlations. Furthermore, we apply the model to estimate functional connectivity for twenty subjects using resting-state fMRI data. Results show that our model provides a richer representation of functional connectivity as compared to considering partial correlations alone. Finally, we demonstrate how our approach can be extended in several ways, for instance to achieve data fusion by informing the conditional independence graph with data from probabilistic tractography. As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results. This reveals that while we are able to infer a clear backbone of connectivity in our empirical results, the data are not accurately described by simply looking at the mode of the distribution over connectivity. The implication of this is that deterministic alternatives may misjudge connectivity results by drawing conclusions from noisy and limited data.

No MeSH data available.


Subcortical connectivity for one subject using the data fusion model.From left to right: the empirical streamline log-counts, the mean posterior connection probability matrix and the mean posterior partial correlation matrix. Note the reduction in connectivity, in particular between the hemispheres, compared to Fig 7. The connections for the left hemisphere (LH) and the right hemisphere (RH) are separated by the dashed lines.
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pcbi.1004534.g008: Subcortical connectivity for one subject using the data fusion model.From left to right: the empirical streamline log-counts, the mean posterior connection probability matrix and the mean posterior partial correlation matrix. Note the reduction in connectivity, in particular between the hemispheres, compared to Fig 7. The connections for the left hemisphere (LH) and the right hemisphere (RH) are separated by the dashed lines.

Mentions: Similar to the previous section, functional connectivity was again estimated for all twenty subjects, but this time using the data fusion approach. This implies that the conditional independence graph is now interpreted as an estimate of structural connectivity, informed by both resting state fMRI as well as probabilistic tractography. In Fig 8, the adjacency matrices of the mean posterior estimates are shown for the same subject as used previously. Overall, the same backbone of functional connectivity is visible as when using only the fMRI data. However, there are a number of differences. In particular, adding information from probabilistic streamlines leads to substantially sparser mean network density: for this subject the density drops to 0.46 (SD = 0.02). In addition, particular connections change from predominantly absent to predominantly present, and vice versa. Fig 9 shows for this subject some of the connections with the largest difference in mean posterior partial correlation. This indicates that the addition of tractography data can both add and remove connections. In general however, we see that the dependencies that are removed due to the addition of tractography data, are those that supported small partial correlations.


Bayesian Estimation of Conditional Independence Graphs Improves Functional Connectivity Estimates.

Hinne M, Janssen RJ, Heskes T, van Gerven MA - PLoS Comput. Biol. (2015)

Subcortical connectivity for one subject using the data fusion model.From left to right: the empirical streamline log-counts, the mean posterior connection probability matrix and the mean posterior partial correlation matrix. Note the reduction in connectivity, in particular between the hemispheres, compared to Fig 7. The connections for the left hemisphere (LH) and the right hemisphere (RH) are separated by the dashed lines.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4634993&req=5

pcbi.1004534.g008: Subcortical connectivity for one subject using the data fusion model.From left to right: the empirical streamline log-counts, the mean posterior connection probability matrix and the mean posterior partial correlation matrix. Note the reduction in connectivity, in particular between the hemispheres, compared to Fig 7. The connections for the left hemisphere (LH) and the right hemisphere (RH) are separated by the dashed lines.
Mentions: Similar to the previous section, functional connectivity was again estimated for all twenty subjects, but this time using the data fusion approach. This implies that the conditional independence graph is now interpreted as an estimate of structural connectivity, informed by both resting state fMRI as well as probabilistic tractography. In Fig 8, the adjacency matrices of the mean posterior estimates are shown for the same subject as used previously. Overall, the same backbone of functional connectivity is visible as when using only the fMRI data. However, there are a number of differences. In particular, adding information from probabilistic streamlines leads to substantially sparser mean network density: for this subject the density drops to 0.46 (SD = 0.02). In addition, particular connections change from predominantly absent to predominantly present, and vice versa. Fig 9 shows for this subject some of the connections with the largest difference in mean posterior partial correlation. This indicates that the addition of tractography data can both add and remove connections. In general however, we see that the dependencies that are removed due to the addition of tractography data, are those that supported small partial correlations.

Bottom Line: A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections.As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results.The implication of this is that deterministic alternatives may misjudge connectivity results by drawing conclusions from noisy and limited data.

View Article: PubMed Central - PubMed

Affiliation: Radboud University, Institute for Computing and Information Sciences, Nijmegen, the Netherlands.

ABSTRACT
Functional connectivity concerns the correlated activity between neuronal populations in spatially segregated regions of the brain, which may be studied using functional magnetic resonance imaging (fMRI). This coupled activity is conveniently expressed using covariance, but this measure fails to distinguish between direct and indirect effects. A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections. Importantly, provided the data are normally distributed, if two variables are conditionally independent given all other variables, their respective partial correlation is zero. In this paper, we propose a probabilistic generative model that allows us to estimate functional connectivity in terms of both partial correlations and a graph representing conditional independencies. Simulation results show that this methodology is able to outperform the graphical LASSO, which is the de facto standard for estimating partial correlations. Furthermore, we apply the model to estimate functional connectivity for twenty subjects using resting-state fMRI data. Results show that our model provides a richer representation of functional connectivity as compared to considering partial correlations alone. Finally, we demonstrate how our approach can be extended in several ways, for instance to achieve data fusion by informing the conditional independence graph with data from probabilistic tractography. As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results. This reveals that while we are able to infer a clear backbone of connectivity in our empirical results, the data are not accurately described by simply looking at the mode of the distribution over connectivity. The implication of this is that deterministic alternatives may misjudge connectivity results by drawing conclusions from noisy and limited data.

No MeSH data available.