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A Gradient Algorithm Locally Equivalent to the Em Algorithm
Open accessAbstract
SUMMARY: In many problems of maximum likelihood estimation, it is impossible to carry out either the E-step or the M-step of the EM algorithm. The present paper introduces a gradient algorithm that is closely related to the EM algorithm. This EM gradient algorithm approximately solves the M-step of the EM algorithm by one iteration of Newton's method. Since Newton's method converges quickly, the local properties of the EM gradient algorithm are almost identical with those of the EM algorithm. Any strict local maximum point of the observed likelihood locally attracts the EM and EM gradient algorithm at the same rate of convergence, and near the maximum point the EM gradient algorithm always produces an increase in the likelihood. With proper modification the EM gradient algorithm also exhibits global convergence properties that are similar to those of the EM algorithm. Our proof of global convergence applies and improves existing theory for the EM algorithm. These theoretical points are reinforced by a discussion of three realistic examples illustrating how the EM gradient algorithm can succeed where the EM algorithm is intractable.
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Cites
Sufficient conditions for the convergence of monotonic mathematicalprogramming algorithms
Meyer, R. R. (1976) · Journal of Computer and System Sciences · doi:10.1016/s0022-0000(76)80021-9 · Cited by 113
Cited by
Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning
Sun, Y., Babu, P., & Palomar, D. P. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2016.2601299 · Cited by 1,820
Hand, D. J. (2007) · Drug Safety · doi:10.2165/00002018-200730070-00010 · Cited by 1,044
The EM Algorithm—an Old Folk-song Sung to a Fast New Tune
Meng, X.-L., & Van Dyk, D. (1997) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00082 · Cited by 802
On-Line Expectation–Maximization Algorithm for latent Data Models
Cappé, O., & Moulines, E. (2009) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2009.00698.x · Cited by 477
Parameter expansion to accelerate EM: the PX-EM algorithm
Liu, C. (1998) · Biometrika · doi:10.1093/biomet/85.4.755 · Cited by 433
Metadata
- Authors
- Lange, K.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1995-07-01
- Volume
- 57
- Issue
- 2
- Pages
- 425-437
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W194242946
- Cited by
- 376
- References
- 1
- FWCI
- 13.40
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Lange, K. (1995). A Gradient Algorithm Locally Equivalent to the Em Algorithm. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1995.tb02037.x
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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