# Estimating Gaussian mixtures using sparse polynomial moment systems

@inproceedings{Lindberg2021EstimatingGM, title={Estimating Gaussian mixtures using sparse polynomial moment systems}, author={Julia Lindberg and Carlos Am'endola and Jose Israel Rodriguez}, year={2021} }

The method of moments is a statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding identifiability asks how many moment equations are needed to get finitely many solutions and how many solutions there are. We answer this question for classes of Gaussian mixture models using the tools of polyhedral geometry. Using these results, we present an algorithm that…

## 2 Citations

### Tensor Moments of Gaussian Mixture Models: Theory and Applications

- Computer Science, MathematicsArXiv
- 2022

This work develops theory and numerical methods for implicit computations with moment tensors of GMMs, reducing the computational and storage costs to O(n) and O( n3), respectively, for general covariance matrices, and for diagonal ones.

### Certifying zeros of polynomial systems using interval arithmetic

- Computer Science, Mathematics
- 2020

The software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated solution to a square system of polynomial equations, which dramatically outperforms earlier approaches to certification.

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