I am currently working on my bachelor thesis and I came across a sufficient statistic,
φ : X × Y → H of y | x
where X is a candidate set in this case strings, Y is a binary property space: {-1,1}, H is a Hilbert Space.
I understand that φ is sufficient if it does not depend on y | x but I just can’t grasp how a sufficient statistic could be constructed here. Any help would be appreciated!