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Variational Bayesian causal connectivity analysis for fMRI.

Luessi M, Babacan SD, Molina R, Booth JR, Katsaggelos AK - Front Neuroinform (2014)

Bottom Line: The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience.We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data.Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm.

View Article: PubMed Central - PubMed

Affiliation: Athinoula A. Martinos Center for Biomedical Imaging, Harvard Medical School, Massachusetts General Hospital Charlestown, MA, USA ; Department of Electrical Engineering and Computer Science, Northwestern University Evanston, IL, USA.

ABSTRACT
The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

No MeSH data available.


Related in: MedlinePlus

Area under ROC curve (AUC) and d-Accuracy scores for data generated by VAR processes with orders from 1 to 7. The proposed method and the Wiener–Granger causality method are denoted by VBCCA(P) and WGCA(P), respectively, where P denotes the VAR model order used in the algorithm. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.
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Figure 3: Area under ROC curve (AUC) and d-Accuracy scores for data generated by VAR processes with orders from 1 to 7. The proposed method and the Wiener–Granger causality method are denoted by VBCCA(P) and WGCA(P), respectively, where P denotes the VAR model order used in the algorithm. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.

Mentions: An important question is how the performance is affected by a mismatch in the VAR order present in the data and the VAR order assumed in the algorithm. For this evaluation we generate simulated data using the same procedure as in the first experiment for N = 25 and an SNR of 0 dB, but we vary the VAR order from 1 to 7. The generated data is used as input to the evaluated methods for which we vary the VAR order used in the algorithm in the same range, i.e., from 1 to 7. Results for this simulation are shown in Figure 3; it can be seen that the proposed method typically outperforms the WGCA method even if there is a mismatch between the VAR order in the data and the VAR order used in the algorithm. It is also interesting to note that the proposed method typically performs well as long as the VAR order used in the algorithm is equal or higher than that present in the data. This behavior can be attributed to two factors. First, the proposed method employs a grouping of VAR coefficients across lags through shared priors, which limits the model complexity even when the VAR order is increased. Second, we use an approximation to the posterior distribution to estimate the VAR coefficients; it is well known that methods which draw inference based on the posterior distribution are less prone to over-fitting than other methods, such as, maximum likelihood methods.


Variational Bayesian causal connectivity analysis for fMRI.

Luessi M, Babacan SD, Molina R, Booth JR, Katsaggelos AK - Front Neuroinform (2014)

Area under ROC curve (AUC) and d-Accuracy scores for data generated by VAR processes with orders from 1 to 7. The proposed method and the Wiener–Granger causality method are denoted by VBCCA(P) and WGCA(P), respectively, where P denotes the VAR model order used in the algorithm. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4017144&req=5

Figure 3: Area under ROC curve (AUC) and d-Accuracy scores for data generated by VAR processes with orders from 1 to 7. The proposed method and the Wiener–Granger causality method are denoted by VBCCA(P) and WGCA(P), respectively, where P denotes the VAR model order used in the algorithm. All results are averages over 50 simulations with error bars indicating the 95% confidence intervals. The average scores are also shown as numerical values in the bar plot, where the values in parentheses are the size of one side of the confidence interval.
Mentions: An important question is how the performance is affected by a mismatch in the VAR order present in the data and the VAR order assumed in the algorithm. For this evaluation we generate simulated data using the same procedure as in the first experiment for N = 25 and an SNR of 0 dB, but we vary the VAR order from 1 to 7. The generated data is used as input to the evaluated methods for which we vary the VAR order used in the algorithm in the same range, i.e., from 1 to 7. Results for this simulation are shown in Figure 3; it can be seen that the proposed method typically outperforms the WGCA method even if there is a mismatch between the VAR order in the data and the VAR order used in the algorithm. It is also interesting to note that the proposed method typically performs well as long as the VAR order used in the algorithm is equal or higher than that present in the data. This behavior can be attributed to two factors. First, the proposed method employs a grouping of VAR coefficients across lags through shared priors, which limits the model complexity even when the VAR order is increased. Second, we use an approximation to the posterior distribution to estimate the VAR coefficients; it is well known that methods which draw inference based on the posterior distribution are less prone to over-fitting than other methods, such as, maximum likelihood methods.

Bottom Line: The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience.We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data.Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm.

View Article: PubMed Central - PubMed

Affiliation: Athinoula A. Martinos Center for Biomedical Imaging, Harvard Medical School, Massachusetts General Hospital Charlestown, MA, USA ; Department of Electrical Engineering and Computer Science, Northwestern University Evanston, IL, USA.

ABSTRACT
The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

No MeSH data available.


Related in: MedlinePlus