Convex Relaxation of Mixture Regression with Efficient Algorithms
Abstract
We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.
Cite
Text
Quadrianto et al. "Convex Relaxation of Mixture Regression with Efficient Algorithms." Neural Information Processing Systems, 2009.Markdown
[Quadrianto et al. "Convex Relaxation of Mixture Regression with Efficient Algorithms." Neural Information Processing Systems, 2009.](https://mlanthology.org/neurips/2009/quadrianto2009neurips-convex/)BibTeX
@inproceedings{quadrianto2009neurips-convex,
title = {{Convex Relaxation of Mixture Regression with Efficient Algorithms}},
author = {Quadrianto, Novi and Lim, John and Schuurmans, Dale and Caetano, Tibério S.},
booktitle = {Neural Information Processing Systems},
year = {2009},
pages = {1491-1499},
url = {https://mlanthology.org/neurips/2009/quadrianto2009neurips-convex/}
}