# Tensor decomposition for learning Gaussian mixtures from moments

arXiv: https://arxiv.org/abs/2106.00555 · HTML: https://mlsanity.com/paper/2106.00555/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 71 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Introduction to Tensor Decompositions and their Applications in Machine Learning](https://mlsanity.com/paper/1711.10781/) (2017)
- [Spectral Learning on Matrices and Tensors](https://mlsanity.com/paper/2004.07984/) (2020)
- [Subspace power method for symmetric tensor decomposition](https://mlsanity.com/paper/1912.04007/) (2019)
- [Clustering Patients with Tensor Decomposition](https://mlsanity.com/paper/1708.08994/) (2017)
- [Model-Based Hierarchical Clustering](https://mlsanity.com/paper/1301.3899/) (2013)
- [Riemannian Newton optimization methods for the symmetric tensor approximation problem](https://mlsanity.com/paper/2003.01469/) (2020)

## Built on by (most cited first, 5 of 5)

- [Faster Robust Tensor Power Method for Arbitrary Order](https://mlsanity.com/paper/2306.00406/) (2023)
- [Tensor Moments of Gaussian Mixture Models: Theory and Applications](https://mlsanity.com/paper/2202.06930/) (2022)
- [Moment Estimation for Nonparametric Mixture Models Through Implicit Tensor Decomposition](https://mlsanity.com/paper/2210.14386/) (2022)
- [A Nested Matrix-Tensor Model for Noisy Multi-view Clustering](https://mlsanity.com/paper/2305.19992/) (2023)
- [Mixtures Closest to a Given Measure: A Semidefinite Programming Approach](https://mlsanity.com/paper/2509.22879/) (2025)

## Abstract (arXiv)

In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric tensor decomposition methods for tackling this problem, where the tensor is built from empirical moments of the data distribution. We consider identifiable tensors, which have a unique decomposition, showing that moment tensors built from spherical Gaussian mixtures have this property. We prove that symmetric tensors with interpolation degree strictly less than half their order are identifiable and we present an algorithm, based on simple linear algebra operations, to compute their decomposition. Illustrative experimentations show the impact of the tensor decomposition method for recovering Gaussian mixtures, in comparison with other state-of-the-art approaches.