Quantum-inspired tensor completion

Matrix completion involves filling in missing entries of a matrix. We shall consider this in the online setting. That is, at each time step, we receive a matrix entry, predict its value and receive its true label. Clearly, it is impossible to give a meaningful learning guarantee if we do not impose any constraints on the matrix structure. Common constraints include low rankness, and we shall consider a related measure called the margin complexity. There already exists a quantum-inspired approach for the matrix case, which is based on regularising the loss function with the quantum relative entropy. We have extended this to various settings, with the inclusion of side information and noise. We will also attempt to perform tensor completion with a suitably adapted version of this algorithm.