@@ -20,5 +20,14 @@ Correlation maps between actual and predicted activation were constructed for ea

### 3. Comparison of prediction using residual bases and original bases

All the above results are based on using residual bases to predict residual task activation maps. To investigate how it improves model accuracy compared to using original bases (to predict original task activation maps), we added the effect of group-level task activation maps back to the residual maps (both residual and predicted) so that the two approaches are comparable. We saw that using residual bases to predict task activation further improves model accuracy ([Figure 9](figs/ukb_addback.png): UKB data; [Figure 10](figs/hcp_addback.png): HCP data). Yellow boxes: correlation between actual and predicted task activations (using residual bases) with group-level effects added back; Blue boxes: correlation between actual and predicted task activations (using original bases).

All the above results are based on using residual bases to predict residual task activation maps. To investigate how it improves model accuracy compared to using original bases (to predict original task activation maps), we added the effect of group-level task activation maps back to the residual maps (both residual and predicted) so that the two approaches are comparable.

* We saw that using residual bases to predict task activation further improves model accuracy ([Figure 9](figs/ukb_addback.png): UKB data; [Figure 10](figs/hcp_addback.png): HCP data). Yellow boxes: correlation between actual and predicted task activations (using residual bases) with group-level effects added back; Blue boxes: correlation between actual and predicted task activations (using original bases).

* To quantify how the diagonals of the correlation matrices differentiates from the off diagonal elements, we calculated the Kolmogorov–Smirnov test statistic as a measure of distance between the distributions of diagonal elements and off-diagonal elements (for a given sample size this statistic provides a comparable distance metric). We found using residual bases to make predictions further enhances the diagonal correlations ([Figure 11](figs/ukb_diag.png): UKB data; [Figure 12](figs/hcp_diag.png)), suggesting it has added advantage in capturing the individual variability in how subjects respond to tasks.