Bayesian deconvolution of [corrected] fMRI data using bilinear dynamical systems.
Bibliographic record
Abstract
In Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983-993], a particular case of the Linear Dynamical Systems (LDSs) was used to model the dynamic behavior of the BOLD response in functional MRI. This state-space model, called bilinear dynamical system (BDS), is used to deconvolve the fMRI time series in order to estimate the neuronal response induced by the different stimuli of the experimental paradigm. The BDS model parameters are estimated using an expectation-maximization (EM) algorithm proposed by Ghahramani and Hinton [Ghahramani, Z., Hinton, G.E. 1996. Parameter Estimation for Linear Dynamical Systems. Technical Report, Department of Computer Science, University of Toronto]. In this paper we introduce modifications to the BDS model in order to explicitly model the spatial variations of the haemodynamic response function (HRF) in the brain using a non-parametric approach. While in Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983-993] the relationship between neuronal activation and fMRI signals is formulated as a first-order convolution with a kernel expansion using basis functions (typically two or three), in this paper, we argue in favor of a spatially adaptive GLM in which a local non-parametric estimation of the HRF is performed. Furthermore, in order to overcome the overfitting problem typically associated with simple EM estimates, we propose a full Variational Bayes (VB) solution to infer the BDS model parameters. We demonstrate the usefulness of our model which is able to estimate both the neuronal activity and the haemodynamic response function in every voxel of the brain. We first examine the behavior of this approach when applied to simulated data with different temporal and noise features. As an example we will show how this method can be used to improve interpretability of estimates from an independent component analysis (ICA) analysis of fMRI data. We finally demonstrate its use on real fMRI data in one slice of the brain.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".