A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians

@article{Dasgupta2007APA,
  title={A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians},
  author={Sanjoy Dasgupta and Leonard J. Schulman},
  journal={J. Mach. Learn. Res.},
  year={2007},
  volume={8},
  pages={203-226}
}
We show that, given data from a mixture of k well-separated spherical Gaussians in ℜd, a simple two-round variant of EM will, with high probability, learn the parameters of the Gaussians to near-optimal precision, if the dimension is high (d >> ln k). We relate this to previous theoretical and empirical work on the EM algorithm. 

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References

Publications referenced by this paper.
SHOWING 1-10 OF 19 REFERENCES

Clustering to Minimize the Maximum Intercluster Distance

  • Theor. Comput. Sci.
  • 1985
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Neural Networks for Pattern Recognition

C. Bishop
  • 1995
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

On the convergence properties of the EM algorithm

C.F.J. Wu
  • Annals of Statistics,
  • 1983
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

A spectral algorithm for learning mixtures of distributions

  • The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
VIEW 1 EXCERPT

Learning mixtures of Gaussians

  • 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
  • 1999
VIEW 1 EXCERPT