Divergence-Based Motivation for Online EM and Combining Hidden Variable Models Article Swipe
Ehsan Amid
,
Manfred K. Warmuth
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1902.04107
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1902.04107
Expectation-Maximization (EM) is a prominent approach for parameter estimation of hidden (aka latent) variable models. Given the full batch of data, EM forms an upper-bound of the negative log-likelihood of the model at each iteration and updates to the minimizer of this upper-bound. We first provide a "model level" interpretation of the EM upper-bound as sum of relative entropy divergences to a set of singleton models, induced by the set of observations. Our alternative motivation unifies the "observation level" and the "model level" view of the EM. As a result, we formulate an online version of the EM algorithm by adding an analogous inertia term which corresponds to the relative entropy divergence to the old model. Our motivation is more widely applicable than the previous approaches and leads to simple online updates for mixture of exponential distributions, hidden Markov models, and the first known online update for Kalman filters. Additionally, the finite sample form of the inertia term lets us derive online updates when there is no closed-form solution. Finally, we extend the analysis to the distributed setting where we motivate a systematic way of combining multiple hidden variable models. Experimentally, we validate the results on synthetic as well as real-world datasets.
Related Topics
Concepts
Kullback–Leibler divergence
Upper and lower bounds
Latent variable
Hidden variable theory
Computer science
Expectation–maximization algorithm
Hidden Markov model
Mathematics
Divergence (linguistics)
Hidden semi-Markov model
Variable (mathematics)
Entropy (arrow of time)
Applied mathematics
Mixture model
Algorithm
Markov chain
Artificial intelligence
Markov model
Variable-order Markov model
Statistics
Machine learning
Maximum likelihood
Quantum mechanics
Physics
Mathematical analysis
Quantum
Philosophy
Linguistics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1902.04107
- https://arxiv.org/pdf/1902.04107
- OA Status
- green
- Cited By
- 3
- References
- 30
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2930074589
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2930074589Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.1902.04107Digital Object Identifier
- Title
-
Divergence-Based Motivation for Online EM and Combining Hidden Variable ModelsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-02-11Full publication date if available
- Authors
-
Ehsan Amid, Manfred K. WarmuthList of authors in order
- Landing page
-
https://arxiv.org/abs/1902.04107Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1902.04107Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1902.04107Direct OA link when available
- Concepts
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Kullback–Leibler divergence, Upper and lower bounds, Latent variable, Hidden variable theory, Computer science, Expectation–maximization algorithm, Hidden Markov model, Mathematics, Divergence (linguistics), Hidden semi-Markov model, Variable (mathematics), Entropy (arrow of time), Applied mathematics, Mixture model, Algorithm, Markov chain, Artificial intelligence, Markov model, Variable-order Markov model, Statistics, Machine learning, Maximum likelihood, Quantum mechanics, Physics, Mathematical analysis, Quantum, Philosophy, LinguisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
3Total citation count in OpenAlex
- Citations by year (recent)
-
2022: 1, 2020: 1, 2019: 1Per-year citation counts (last 5 years)
- References (count)
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30Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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