# Manifold Optimization for Gaussian Mixture Models

arXiv: https://arxiv.org/abs/1506.07677 · HTML: https://mlsanity.com/paper/1506.07677/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2015.

## Built on by (most cited first, 1 of 1)

- [Dynamical Wasserstein Barycenters for Time-series Modeling](https://mlsanity.com/paper/2110.06741/) (2021)

## Abstract (arXiv)

We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using Riemannian manifold optimization as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation of manifold optimization, however, fails spectacularly: it converges to the same solution but vastly slower. Driven by intuition from manifold convexity, we then propose a reparamerization that has remarkable empirical consequences. It makes manifold optimization not only match EM---a highly encouraging result in itself given the poor record nonlinear programming methods have had against EM so far---but also outperform EM in many practical settings, while displaying much less variability in running times. We further highlight the strengths of manifold optimization by developing a somewhat tuned manifold LBFGS method that proves even more competitive and reliable than existing manifold optimization tools. We hope that our results encourage a wider consideration of manifold optimization for parameter estimation problems.