A Double Regression Method for Graphical Modeling of High-dimensional Nonlinear and Non-Gaussian Data Article Swipe
Siqi Liang
,
Faming Liang
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.04585
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.04585
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are Gaussian or mixed and the variables are linearly dependent. In this paper, we propose a double regression method for learning graphical models under the high-dimensional nonlinear and non-Gaussian setting, and prove that the proposed method is consistent under mild conditions. The proposed method works by performing a series of nonparametric conditional independence tests. The conditioning set of each test is reduced via a double regression procedure where a model-free sure independence screening procedure or a sparse deep neural network can be employed. The numerical results indicate that the proposed method works well for high-dimensional nonlinear and non-Gaussian data.
Related Topics
Concepts
Independence (probability theory)
Conditional independence
Graphical model
Gaussian
Nonparametric statistics
Mathematics
Nonlinear regression
Nonlinear system
Nonparametric regression
Set (abstract data type)
Computer science
Regression analysis
Algorithm
Focus (optics)
Applied mathematics
Artificial intelligence
Statistics
Quantum mechanics
Physics
Programming language
Optics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2212.04585
- https://arxiv.org/pdf/2212.04585
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4311248568
All OpenAlex metadata
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https://openalex.org/W4311248568Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2212.04585Digital Object Identifier
- Title
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A Double Regression Method for Graphical Modeling of High-dimensional Nonlinear and Non-Gaussian DataWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-12-08Full publication date if available
- Authors
-
Siqi Liang, Faming LiangList of authors in order
- Landing page
-
https://arxiv.org/abs/2212.04585Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2212.04585Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2212.04585Direct OA link when available
- Concepts
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Independence (probability theory), Conditional independence, Graphical model, Gaussian, Nonparametric statistics, Mathematics, Nonlinear regression, Nonlinear system, Nonparametric regression, Set (abstract data type), Computer science, Regression analysis, Algorithm, Focus (optics), Applied mathematics, Artificial intelligence, Statistics, Quantum mechanics, Physics, Programming language, OpticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.regression | 54, 102 |
| abstract_inverted_index.statistics | 7 |
| abstract_inverted_index.variables. | 22 |
| abstract_inverted_index.conditional | 13, 88 |
| abstract_inverted_index.conditions. | 77 |
| abstract_inverted_index.conditioning | 92 |
| abstract_inverted_index.independence | 14, 89, 108 |
| abstract_inverted_index.non-Gaussian | 65, 134 |
| abstract_inverted_index.nonparametric | 87 |
| abstract_inverted_index.relationships | 15 |
| abstract_inverted_index.high-dimensional | 62, 131 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.16175728 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |