Ground truth functional region nilearn haxby dataset

Hi all, this is my first question on the forum, so feel free to ignore it if it is not relevant,

I am doing research on sparse recovery, and wanted to compare some sparse recovery methods (similar to Lasso etc) using the tutorial from the hidimstat package, which, here uses the Haxby dataset with Nilearn to reconstruct a functional region: using methods similar to Lasso, they reconstruct some functional brain region from a dataset (X, y) where targets y are from the classes ‘face’ and ‘house’. The functional region is supposed to be the “true” model w*, if the data is generated as y = <x, w*> + epsilon.

My question is: I am not familiar with brain imaging, but I was wondering if by any chance there is a ground truth on what is the true functional region associated with such task ? (i.e. what is the true w*, or at least the true support of w* ?) (my ultimate goal would be to use it to evaluate more quantitatively the quality of support recovery of our methods)

In the end of the tutorial, they say that their method “seem to recover the visual cortex”, so I was thinking that maybe this means the ground truth from that task could be a “mask” from the haxby dataset ? For instance I saw that there is haxby_dataset.mask_house[0] or haxby_dataset.mask_face[0] in that Nilearn tutorial

However, these are two masks, so I was wondering if there was a single mask, that would correspond to the supposedly true model w* (i.e. maybe a mask for the visual cortex ?) Could such mask be considered a ground truth for the hidimstat task above described ?

Thanks a lot in advance for your help !