A fundamental structural model for data is that the data points lie close to an unknown subspace, meaning that the matrix created by concatenating the data vectors has low rank. We address a particular low-rank matrix recovery problem where we wish to recover a set of vectors from a low-dimensional subspace after they have been individually compressed (or "sketched").

Hence, the function over this constraint set isG-Lipschitz. Finally, in Lemma6, we provide bounds on excess empirical risk and average regret of gradient descent. Let ℓ be a non-negative eH smooth convex loss function. Let bw:= A(S), S(i) be the dataset where thei-th data point is replaced by an i.i.d. A.4 HighDimensionProofofTheorem 2. Let α 1 be a parameter to be set later.

We study the problem of(ǫ,δ)-differentially private learning of linear predictors with convexlosses.

These assumptions imply that an optimal solutionx?