Affinely Parametrized State-space Models: Ways to Maximize the Likelihood Function Article Swipe
Adrian Wills
,
Chengpu Yu
,
Lennart Ljung
,
Michel Verhaegen
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1016/j.ifacol.2018.09.170
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1016/j.ifacol.2018.09.170
Using Maximum Likelihood (or Prediction Error) methods to identify linear state space model is a prime technique. The likelihood function is a nonconvex function and care must be exercised in the numerical maximization. Here the focus will be on affine parameterizations which allow some special techniques and algorithms. Three approaches to formulate and perform the maximization are described in this contribution: (1) The standard and well known Gauss-Newton iterative search, (2) a scheme based on the EM (expectation-maximization) technique, which becomes especially simple in the affine parameterization case, and (3) a new approach based on lifting the problem to a higher dimension in the parameter space and introducing rank constraints.
Related Topics
Concepts
Maximization
Likelihood function
Affine transformation
Expectation–maximization algorithm
Dimension (graph theory)
Rank (graph theory)
Mathematical optimization
State space
Mathematics
Function (biology)
Focus (optics)
Simple (philosophy)
Space (punctuation)
Prime (order theory)
Applied mathematics
State (computer science)
Computer science
Algorithm
Estimation theory
Maximum likelihood
Statistics
Pure mathematics
Philosophy
Combinatorics
Evolutionary biology
Physics
Operating system
Epistemology
Optics
Biology
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.ifacol.2018.09.170
- OA Status
- diamond
- Cited By
- 5
- References
- 23
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2895806851
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2895806851Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1016/j.ifacol.2018.09.170Digital Object Identifier
- Title
-
Affinely Parametrized State-space Models: Ways to Maximize the Likelihood FunctionWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2018Year of publication
- Publication date
-
2018-01-01Full publication date if available
- Authors
-
Adrian Wills, Chengpu Yu, Lennart Ljung, Michel VerhaegenList of authors in order
- Landing page
-
https://doi.org/10.1016/j.ifacol.2018.09.170Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
diamondOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1016/j.ifacol.2018.09.170Direct OA link when available
- Concepts
-
Maximization, Likelihood function, Affine transformation, Expectation–maximization algorithm, Dimension (graph theory), Rank (graph theory), Mathematical optimization, State space, Mathematics, Function (biology), Focus (optics), Simple (philosophy), Space (punctuation), Prime (order theory), Applied mathematics, State (computer science), Computer science, Algorithm, Estimation theory, Maximum likelihood, Statistics, Pure mathematics, Philosophy, Combinatorics, Evolutionary biology, Physics, Operating system, Epistemology, Optics, BiologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
5Total citation count in OpenAlex
- Citations by year (recent)
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2024: 1, 2023: 1, 2019: 3Per-year citation counts (last 5 years)
- References (count)
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23Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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