Nonlinear Function Estimation with Empirical Bayes and Approximate Message Passing Article Swipe
Hangjin Liu
,
Zhou
,
Ahmad Beirami
,
Dror Baron
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1907.02482
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1907.02482
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels increase the feature set, and may result in poorly conditioned matrices. Nonetheless, we show several examples where the matrix in our linear inverse problem contains only mild linear correlations among columns. The coefficients vector is modeled within a Bayesian setting for which approximate message passing (AMP), an algorithmic framework for signal reconstruction, offers Bayes-optimal signal reconstruction quality. While the Bayesian setting limits the scope of our work, it is a first step toward estimation of real world nonlinear functions. The coefficients vector is estimated using two AMP-based approaches, a Bayesian one and empirical Bayes. Numerical results confirm that our AMP-based approaches learn the function better than LASSO, offering markedly lower error in predicting test data.
Related Topics
Concepts
Bayes' theorem
Nonlinear system
Lasso (programming language)
Algorithm
Kernel (algebra)
Computer science
Bayesian probability
Mathematics
Bayes estimator
Function (biology)
Mathematical optimization
Polynomial kernel
Inverse problem
Applied mathematics
Artificial intelligence
Kernel method
Machine learning
Support vector machine
Physics
Mathematical analysis
Quantum mechanics
Combinatorics
World Wide Web
Biology
Evolutionary biology
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1907.02482
- https://arxiv.org/pdf/1907.02482
- OA Status
- green
- References
- 29
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2979097212
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W2979097212Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.1907.02482Digital Object Identifier
- Title
-
Nonlinear Function Estimation with Empirical Bayes and Approximate Message PassingWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-07-04Full publication date if available
- Authors
-
Hangjin Liu, Zhou, Ahmad Beirami, Dror BaronList of authors in order
- Landing page
-
https://arxiv.org/abs/1907.02482Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1907.02482Direct 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/1907.02482Direct OA link when available
- Concepts
-
Bayes' theorem, Nonlinear system, Lasso (programming language), Algorithm, Kernel (algebra), Computer science, Bayesian probability, Mathematics, Bayes estimator, Function (biology), Mathematical optimization, Polynomial kernel, Inverse problem, Applied mathematics, Artificial intelligence, Kernel method, Machine learning, Support vector machine, Physics, Mathematical analysis, Quantum mechanics, Combinatorics, World Wide Web, Biology, Evolutionary biologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
29Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/1907.02482 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/1907.02482 |
| publication_date | 2019-07-04 |
| publication_year | 2019 |
| referenced_works | https://openalex.org/W2149925139, https://openalex.org/W2138358551, https://openalex.org/W2155549765, https://openalex.org/W2543631487, https://openalex.org/W2095865158, https://openalex.org/W574918892, https://openalex.org/W2111146558, https://openalex.org/W3098848552, https://openalex.org/W1995834279, https://openalex.org/W2891034694, https://openalex.org/W2135046866, https://openalex.org/W2022873843, https://openalex.org/W2965130990, https://openalex.org/W2109657485, https://openalex.org/W2083429100, https://openalex.org/W2134717973, https://openalex.org/W2550925785, https://openalex.org/W2064385888, https://openalex.org/W2125520394, https://openalex.org/W2481342515, https://openalex.org/W2964047892, https://openalex.org/W2135859872, https://openalex.org/W2144015943, https://openalex.org/W1855388283, https://openalex.org/W2964296776, https://openalex.org/W2082029531, https://openalex.org/W2090842051, https://openalex.org/W1480376833, https://openalex.org/W2161597212 |
| referenced_works_count | 29 |
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| abstract_inverted_index.it | 102 |
| abstract_inverted_index.of | 99, 109 |
| abstract_inverted_index.to | 5, 13, 24 |
| abstract_inverted_index.we | 18, 47 |
| abstract_inverted_index.The | 66, 114 |
| abstract_inverted_index.and | 39, 126 |
| abstract_inverted_index.for | 75, 84 |
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| abstract_inverted_index.one | 27, 125 |
| abstract_inverted_index.our | 55, 100, 133 |
| abstract_inverted_index.the | 36, 52, 93, 97, 137 |
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| abstract_inverted_index.LASSO, | 141 |
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| abstract_inverted_index.toward | 107 |
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| abstract_inverted_index.Nonlinear | 0 |
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| abstract_inverted_index.reconstruction, | 86 |
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