Tensor completion aims at filling the missing or unobserved entries based on
partially observed tensors. However, utilization of the observed tensors often
raises serious privacy concerns in many practical scenarios. To address this
issue, we propose a solid and unified framework that contains several
approaches for applying differential privacy to the two most widely used tensor
decomposition methods: i) CANDECOMP/PARAFAC~(CP) and ii) Tucker decompositions.
For each approach, we establish a rigorous privacy guarantee and meanwhile
evaluate the privacy-accuracy trade-off. Experiments on synthetic and
real-world datasets demonstrate that our proposal achieves high accuracy for
tensor completion while ensuring strong privacy protections.

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