In this setting, the arms arrive in a stream, and the number of arms that can be storedinthememory atanytime,isbounded.

's are real-valued weights depending on the accuracy of h

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Wealsoshow thatacertified version ofthecomputationally tractable DOO algorithm matches these packing and integral bounds.

One such prior on the low-rank component is sparsity, giving rise to the sparse principal component analysis problem. Unfortunately, there is strong evidence that this problem suffers from a computational-to-statistical gap, which may be fundamental. In this work, we study an alternative prior where the low-rank component is in the range of a trained generative network.

First wecharacterize theinformation-theoretic sharp threshold on the minimum number of observed matrix entries required for reliable matrix completion, as a function of the quantified quality (to be detailed) of the considered hierarchical graph side information.