Statistical guarantees for the EM algorithm: From population to sample-based analysis

@article{Balakrishnan2014StatisticalGF,
  title={Statistical guarantees for the EM algorithm: From population to sample-based analysis},
  author={Sivaraman Balakrishnan and M. Wainwright and Bin Yu},
  journal={ArXiv},
  year={2014},
  volume={abs/1408.2156}
}
We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in the limit of infinite data), followed by results that apply to updates based on a finite set of samples. First, we characterize the domain of attraction of any global maximizer of the population likelihood. This characterization is based on a novel view of the… Expand
Singularity, Misspecification, and the Convergence Rate of EM
Ten Steps of EM Suffice for Mixtures of Two Gaussians
Theoretical guarantees for EM under misspecified Gaussian mixture models
Global Analysis of Expectation Maximization for Mixtures of Two Gaussians
Challenges with EM in application to weakly identifiable mixture models
Instability, Computational Efficiency and Statistical Accuracy
Benefits of over-parameterization with EM
Benefits of over-parameterization with EM
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 65 REFERENCES
On the global and componentwise rates of convergence of the EM algorithm
Convergence in Norm for Alternating Expectation-Maximization (EM) Type Algorithms
On Convergence Properties of the EM Algorithm for Gaussian Mixtures
Mixture densities, maximum likelihood, and the EM algorithm
Alternating Minimization for Mixed Linear Regression
ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM
...
1
2
3
4
5
...