# Differentially Private Robust Low-Rank Approximation

In this paper, we study the following robust low-rank matrix approximation problem: given a matrix $A \in \R^{n \times d}$, find a rank-$k$ matrix $B$, while satisfying differential privacy, such that $\norm{ A - B }_p \leq \alpha \mathsf{OPT}_k(A) + \tau,$ where $\norm{ M }_p$ is the entry-wise $\ell_p$-norm and $\mathsf{OPT}_k(A):=\min_{\mathsf{rank}(X) \leq k} \norm{ A - X}_p$. It is well known that low-rank approximation w.r.t... (read more)

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