# Provable Sparse Tensor Decomposition

arXiv: https://arxiv.org/abs/1502.01425 · HTML: https://mlsanity.com/paper/1502.01425/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2015.

## Built on by (most cited first, 16 of 16)

- [Provable Tensor-Train Format Tensor Completion by Riemannian Optimization](https://mlsanity.com/paper/2108.12163/) (2021)
- [Learning Good State and Action Representations via Tensor Decomposition](https://mlsanity.com/paper/2105.01136/) (2021)
- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Modelling matrix time series via a tensor CP-decomposition](https://mlsanity.com/paper/2112.15423/) (2021)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression](https://mlsanity.com/paper/2305.06199/) (2023)
- [Jointly Modeling and Clustering Tensors in High Dimensions](https://mlsanity.com/paper/2104.07773/) (2021)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [Two-level monotonic multistage recommender systems](https://mlsanity.com/paper/2110.06116/) (2021)
- [A Probit Tensor Factorization Model For Relational Learning](https://mlsanity.com/paper/2111.03943/) (2021)
- [Decomposable Sparse Tensor on Tensor Regression](https://mlsanity.com/paper/2212.05024/) (2022)
- [Statistical and computational rates in high rank tensor estimation](https://mlsanity.com/paper/2304.04043/) (2023)
- [Guaranteed Noisy CP Tensor Recovery via Riemannian Optimization on the Segre Manifold](https://mlsanity.com/paper/2510.00569/) (2025)
- [Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection](https://mlsanity.com/paper/2605.19122/) (2026)
- [Bayesian Tensor Decomposition with Diffusion Model Prior](https://mlsanity.com/paper/2606.03212/) (2026)

## Abstract (arXiv)

We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family of high dimensional latent variable models, including high dimensional Gaussian mixture and mixtures of sparse regressions. A thorough theoretical investigation is further conducted. In particular, we show that the final decomposition estimator is guaranteed to achieve a local statistical rate, and further strengthen it to the global statistical rate by introducing a proper initialization procedure. In high dimensional regimes, the obtained statistical rate significantly improves those shown in the existing non-sparse decomposition methods. The empirical advantages of TTP are confirmed in extensive simulated results and two real applications of click-through rate prediction and high-dimensional gene clustering.