# Applying Differential Privacy to Tensor Completion

arXiv: https://arxiv.org/abs/2110.00539 · HTML: https://mlsanity.com/paper/2110.00539/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 1 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Differentially Private Empirical Risk Minimization Revisited: Faster and More General](https://mlsanity.com/paper/1802.05251/) (2018)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [Efficient Private ERM for Smooth Objectives](https://mlsanity.com/paper/1703.09947/) (2017)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Fast Differentially Private Matrix Factorization](https://mlsanity.com/paper/1505.01419/) (2015)
- [DP-LSSGD: A Stochastic Optimization Method to Lift the Utility in Privacy-Preserving ERM](https://mlsanity.com/paper/1906.12056/) (2019)
- [Privacy-Preserving Tensor Factorization for Collaborative Health Data Analysis](https://mlsanity.com/paper/1908.09888/) (2019)
- [Online and Differentially-Private Tensor Decomposition](https://mlsanity.com/paper/1606.06237/) (2016)
- [Distributed Differentially-Private Algorithms for Matrix and Tensor Factorization](https://mlsanity.com/paper/1804.10299/) (2018)

## Abstract (arXiv)

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.