# Online and Differentially-Private Tensor Decomposition

arXiv: https://arxiv.org/abs/1606.06237 · HTML: https://mlsanity.com/paper/1606.06237/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2016.

## Built on by (most cited first, 8 of 8)

- [Reconstructing Training Data from Model Gradient, Provably](https://mlsanity.com/paper/2212.03714/) (2022)
- [Optimal Gradient-based Algorithms for Non-concave Bandit Optimization](https://mlsanity.com/paper/2107.04518/) (2021)
- [Faster Robust Tensor Power Method for Arbitrary Order](https://mlsanity.com/paper/2306.00406/) (2023)
- [Tensor decomposition of higher-order correlations by nonlinear Hebbian plasticity](https://mlsanity.com/paper/2106.15685/) (2021)
- [Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation](https://mlsanity.com/paper/2101.04194/) (2021)
- [Sharp Analysis of Power Iteration for Tensor PCA](https://mlsanity.com/paper/2401.01047/) (2024)
- [Applying Differential Privacy to Tensor Completion](https://mlsanity.com/paper/2110.00539/) (2021)
- [Selective Multiple Power Iteration: from Tensor PCA to gradient-based exploration of landscapes](https://mlsanity.com/paper/2112.12306/) (2021)

## Abstract (arXiv)

In this paper, we resolve many of the key algorithmic questions regarding robustness, memory efficiency, and differential privacy of tensor decomposition. We propose simple variants of the tensor power method which enjoy these strong properties. We present the first guarantees for online tensor power method which has a linear memory requirement. Moreover, we present a noise calibrated tensor power method with efficient privacy guarantees. At the heart of all these guarantees lies a careful perturbation analysis derived in this paper which improves up on the existing results significantly.