Fig 1.
Stacking methodology for multi-modal data prediction.
In the first step and for each brain measurement, a 5-fold cross-validation is applied to the training set to simultaneously optimize a LASSO-PCR model and produce out-of-sample training set predictions. The optimized trained LASSO-PCR model is then used to generate predictions from the test set. In the second learning step, training and test set predictions are stacked across channels. A new LASSO model acting on the new training set matrix is then optimized with an inner 5-fold cross-validation and fitted to generate the final predictions on the new test set.
Fig 2.
Single-channel and stacked performances to predict cognition.
The coefficient of determination, R2, between the observed and predicted values of seven cognitive scores using each brain measurement separately and together by stacking their predictions. The scenario that yields the maximum predictive accuracy in out-of-sample tests is shown in red.
Fig 3.
Regression coefficient distribution of each single-channel in the stacked model.
Across the 100 different data splits, the weight distribution assigned to the out-of-sample predictions of each brain measurement by the stacked LASSO model in those cognitive scores in which stacking significantly improved the overall performance.
Fig 4.
Multi-modal neuroimaging patterns from cognitive prediction.
Encoding weight maps of each brain measurement whose contribution to predicting cognitive scores during stacking is statistically non-redundant (N.C. ≡ Non-Contributing). Red and blue colors in the brain images (i.e., local connectome, cortical surface area, cortical thickness, and subcortical volumes) display positive and negative weights respectively. For the resting-state connectivity features the strength maps are instead displayed, estimated as the sum over the rows (or columns) in the absolute matrix of links’ weights, thresholded to concentrate only on their 1% largest values. The weight map for the volumetric properties in Crystallized Intelligence is marked as non-contributing (N.C.) since this channel did not survive after adding the confounders channel to the stacked model.
Table 1.
Main descriptive statistics for the response cognitive variables.