Stacked regressions and structured variance partitioning for interpretable brain maps

Relating brain activity associated with a complex stimulus to different properties of that stimulus is a powerful approach for constructing functional brain maps. However, when stimuli are naturalistic, their properties are often correlated (e.g., visual and semantic features of natural images, or different layers of a convolutional neural network that are used as features of images). Correlated properties can act as confounders for each other and complicate the interpretability of brain maps, and can impact the robustness of statistical estimators. Here, we present an approach for brain mapping based on two proposed methods: stacking different encoding models and structured variance partitioning. Our stacking algorithm combines encoding models that each use as input a feature space that describes a different stimulus attribute. The algorithm learns to predict the activity of a voxel as a linear combination of the outputs of different encoding models. We show that the resulting combined model can predict held-out brain activity better or at least as well as the individual encoding models. Further, the weights of the linear combination are readily interpretable; they show the importance of each feature space for predicting a voxel. We then build on our stacking models to introduce structured variance partitioning, a new type of variance partitioning that takes into account the known relationships between features. Our approach constrains the size of the hypothesis space and allows us to ask targeted questions about the similarity between feature spaces and brain regions even in the presence of correlations between the feature spaces. We validate our approach in simulation, showcase its brain mapping potential on fMRI data, and release a Python package. Our methods can be useful for researchers interested in aligning brain activity with different layers of a neural network, or with other types of correlated feature spaces.