Fig. 8. The role of the network connectivity and external input in reproducing the correlation structure.

For all 100 subjects in the dataset, we generate new data using the learned regional parameters θ^r, but with randomly drawn system and observation noise. We use two models: one trained with the external input and one trained without it. We then generate new data with both external input and network input present (Ext & net), with only the external input present and network connectivity set to zero (Only ext), with only the network input and external input set to zero (Only net), and with neither (None). For each subject, we perform 20 simulations with different noise instantiations. (A) Pearson correlation of the nondiagonal elements of the FC in the original and generated data for the different variants of the models. Each boxplot is constructed from n = 2000 data points. The box extends from the first quartile to the third quartile of the data, with a solid line at the median and dashed line at the mean. The whiskers extend from the box by 1.5× the interquartile range. Fliers are not shown. The differences between all means are statistically significant (two-sided t test, P < 1 × 10⁻¹⁰) except between the two variants without either input. (B) Mean of the nondiagonal elements of the original and simulated FC. Each dot corresponds to the single subject; the FC mean was averaged over the 20 simulations.