# Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality

arXiv: https://arxiv.org/abs/1811.05076 · HTML: https://mlsanity.com/paper/1811.05076/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2018.

## Built on by (most cited first, 15 of 15)

- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Beyond the Signs: Nonparametric Tensor Completion via Sign Series](https://mlsanity.com/paper/2102.00384/) (2021)
- [Stochastic Mirror Descent for Low-Rank Tensor Decomposition Under Non-Euclidean Losses](https://mlsanity.com/paper/2104.14562/) (2021)
- [Efficient Nonparametric Tensor Decomposition for Binary and Count Data](https://mlsanity.com/paper/2401.07711/) (2024)
- [Statistical and Computational Efficiency for Smooth Tensor Estimation with Unknown Permutations](https://mlsanity.com/paper/2111.04681/) (2021)
- [A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion](https://mlsanity.com/paper/2304.13940/) (2023)
- [Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model](https://mlsanity.com/paper/2405.11377/) (2024)
- [Towards Quantum Tensor Decomposition in Biomedical Applications](https://mlsanity.com/paper/2502.13140/) (2025)
- [Rich Insights from Cheap Signals: Efficient Evaluations via Tensor Factorization](https://mlsanity.com/paper/2603.02029/) (2026)
- [Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model](https://mlsanity.com/paper/2307.00575/) (2023)
- [Fourier Low-rank and Sparse Tensor for Efficient Tensor Completion](https://mlsanity.com/paper/2505.11261/) (2025)
- [Statistical and computational rates in high rank tensor estimation](https://mlsanity.com/paper/2304.04043/) (2023)
- [Near-Efficient and Non-Asymptotic Multiway Inference](https://mlsanity.com/paper/2511.05368/) (2025)
- [Generalized Canonical Polyadic Tensor Decompositions with General Symmetry](https://mlsanity.com/paper/2601.05335/) (2026)
- [Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularization](https://mlsanity.com/paper/2606.30958/) (2026)

## Abstract (arXiv)

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estimation method, and obtain the theoretical accuracy guarantees. In contrast to continuous-valued problems, the binary tensor problem exhibits an interesting phase transition phenomenon according to the signal-to-noise ratio. The error bound for the parameter tensor estimation is established, and we show that the obtained rate is minimax optimal under the considered model. Furthermore, we develop an alternating optimization algorithm with convergence guarantees. The efficacy of our approach is demonstrated through both simulations and analyses of multiple data sets on the tasks of tensor completion and clustering.