The Spectral Method for General Mixture Models

Abstract

We present an algorithm for learning a mixture of distributions based on spectral projection. We prove a general property of spectral projection for arbitrary mixtures and show that the resulting algorithm is efficient when the components of the mixture are logconcave distributions in $\Re^{n}$ whose means are separated. The separation required grows with k , the number of components, and log n . This is the first result demonstrating the benefit of spectral projection for general Gaussians and widens the scope of this method. It improves substantially on previous results, which focus either on the special case of spherical Gaussians or require a separation that has a considerably larger dependence on n .

Cite

Text

Kannan et al. "The Spectral Method for General Mixture Models." Annual Conference on Computational Learning Theory, 2005. doi:10.1007/11503415_30

Markdown

[Kannan et al. "The Spectral Method for General Mixture Models." Annual Conference on Computational Learning Theory, 2005.](https://mlanthology.org/colt/2005/kannan2005colt-spectral/) doi:10.1007/11503415_30

BibTeX

@inproceedings{kannan2005colt-spectral,
  title     = {{The Spectral Method for General Mixture Models}},
  author    = {Kannan, Ravindran and Salmasian, Hadi and Vempala, Santosh S.},
  booktitle = {Annual Conference on Computational Learning Theory},
  year      = {2005},
  pages     = {444-457},
  doi       = {10.1007/11503415_30},
  url       = {https://mlanthology.org/colt/2005/kannan2005colt-spectral/}
}