Non-asymptotic model selection in block-diagonal mixture of polynomial\n experts models Article Swipe
TrungTin Nguyen
,
Faïcel Chamroukhi
,
Hien D. Nguyen
,
Florence Forbes
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2104.08959
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2104.08959
Model selection, via penalized likelihood type criteria, is a standard task\nin many statistical inference and machine learning problems. Progress has led\nto deriving criteria with asymptotic consistency results and an increasing\nemphasis on introducing non-asymptotic criteria. We focus on the problem of\nmodeling non-linear relationships in regression data with potential hidden\ngraph-structured interactions between the high-dimensional predictors, within\nthe mixture of experts modeling framework. In order to deal with such a complex\nsituation, we investigate a block-diagonal localized mixture of polynomial\nexperts (BLoMPE) regression model, which is constructed upon an inverse\nregression and block-diagonal structures of the Gaussian expert covariance\nmatrices. We introduce a penalized maximum likelihood selection criterion to\nestimate the unknown conditional density of the regression model. This model\nselection criterion allows us to handle the challenging problem of inferring\nthe number of mixture components, the degree of polynomial mean functions, and\nthe hidden block-diagonal structures of the covariance matrices, which reduces\nthe number of parameters to be estimated and leads to a trade-off between\ncomplexity and sparsity in the model. In particular, we provide a strong\ntheoretical guarantee: a finite-sample oracle inequality satisfied by the\npenalized maximum likelihood estimator with a Jensen-Kullback-Leibler type\nloss, to support the introduced non-asymptotic model selection criterion. The\npenalty shape of this criterion depends on the complexity of the considered\nrandom subcollection of BLoMPE models, including the relevant graph structures,\nthe degree of polynomial mean functions, and the number of mixture components.\n
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- Type
- preprint
- Landing Page
- http://arxiv.org/abs/2104.08959
- https://arxiv.org/pdf/2104.08959
- OA Status
- green
- Cited By
- 2
- References
- 33
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3155215583
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- OpenAlex ID
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https://openalex.org/W3155215583Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2104.08959Digital Object Identifier
- Title
-
Non-asymptotic model selection in block-diagonal mixture of polynomial\n experts modelsWork title
- Type
-
preprintOpenAlex work type
- Publication year
-
2021Year of publication
- Publication date
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2021-04-18Full publication date if available
- Authors
-
TrungTin Nguyen, Faïcel Chamroukhi, Hien D. Nguyen, Florence ForbesList of authors in order
- Landing page
-
https://arxiv.org/abs/2104.08959Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2104.08959Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2104.08959Direct OA link when available
- Concepts
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Diagonal, Selection (genetic algorithm), Block (permutation group theory), Mathematics, Polynomial, Model selection, Applied mathematics, Computer science, Mathematical optimization, Statistics, Combinatorics, Artificial intelligence, Mathematical analysis, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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2Total citation count in OpenAlex
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2024: 1, 2022: 1Per-year citation counts (last 5 years)
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33Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| referenced_works_count | 33 |
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