Many data applications have certain invariant constraints due to practical needs. Data curators who employ differential privacy need respect such on the sanitized product as a primary utility requirement. Invariants challenge formulation, implementation, and interpretation of guarantees. We propose subspace privacy, honestly characterize dependence output confidential aspects data. discuss two ...

We consider maximal operators associated to singular averages along finite subsets Σ of the Grassmannian Gr(d,n) d-dimensional subspaces Rn. The well studied d=1 case corresponds directional function with respect arbitrary Gr(1,n)=Sn−1. provide a systematic study all cases 1≤d<n and prove essentially sharp L2(Rn) bounds for subspace averaging operator in terms cardinality Σ, no assumption on st...