Prediction of task

To ensure that our method of reverse inference not only fit the original data, but also picked up on task specific differences, we used the correlation matrix of the cognitive components' probabilities across time, and each component's mean activity in the task (relative to the mean of that component in that subject in other tasks), to predict which task the subject is executing. Thus the model contains 78 unique features. We have 600 of these feature sets; 6 per subject. We iteratively split the data into 450 feature sets and 150 feature sets, fitting the model to the 450 feature sets and then testing the model on the 150 feature sets. We did this 10,000 times, saving the accuracy of the model to predict the task of the unseen matrices. We measured accuracy with precision. The precision is the ratio tp / (tp + fp) where tp is the number of true positives and fp the number of false positives. Intuitively, the precision is the ability of the classifier not to label as positive a sample that is negative. The best value is 1 and the worst value is 0 \cite{scikit-learn}.

Analysis of components engaged

One of our previous analyses \cite{26598686} using the author-topic model of BrainMap showed that, when more components are engaged in a task, activity at connector nodes--regions mostly in the fronto-parietal network--is increased. This analysis was across BrainMap tasks, which are themselves the mean across multiple experiments, each of which averages across individuals, and is a contrast of that task, relative to another task. Here, we were able to do a more thorough analysis at a higher temporal resolution in individual subjects. Moreover, instead of taking the mean activity across a certain set of regions (as the meta-data contains a large amount of 0 values) we were able to simply correlate each voxel's activity with the number of components engaged at each time point, which we measured with 1 minus the standard deviation of the distribution of component probability values. We also executed this analysis where we set voxels in the original data to zero if 3 or more components have a high probability of being engaged at the voxel (> 1e-5). This ensures that the estimate of the number of components engaged is driven by voxels that are relatively specialized to a single component, and not driven by voxels where many components have a high probability, as these areas overlap highly with connector nodes \cite{26598686}, which is precisely where we expect to see increased activity as more components are engaged. 

States

We sought to reduce individual time-points into states. Given our joint probabilistic reverse inference model, for each task, for each subject, for each time point, we have the distribution of component probabilities. For each time point i and j in a particular subject and task, we calculate the correlation between their distributions. This is done for each pair of time points, resulting in a square correlation matrix. This matrix is then used to form a graph, where each node is a time point and each edge is the similarity of the time points' component probability distributions. Community detection is then applied to cluster time points into communities. The edges weights are raised to a particular exponent to more heavily weight the strong connections; higher exponents lead to a greater number of communities while using InfoMap. The exponent is raised until the number of communities preferred is reached. We chose to analyze 8 communities or states. For each community, we then take the mean of all time points in that community. For each of these images (i.e., all the mean images from all the subjects), we compute the joint probabilistic reverse inference. The same graph construction and community detection procedure above is then applied, treating each mean image from a subject as a node, giving us a final clustering of original brain data into states.

Results

Joint Probabilistic Reverse Inference can accurately capture which components are engaged and model the original data

For each task, for each subject, for each frame, we measured the fit of the model to the data. The fit, on average, across tasks, was 0.29. Essentially, this value is the spatial correlation between the model's reduction of the data, and the original data. In all tasks, the model fits the data it was fit significantly better than data it was not fit to. Thus, the model was able to fit the data with accuracy across tasks (Figure 3).