Bayesian Nonlinear Function Estimation with Approximate Message Passing Article Swipe
In many areas, massive amounts of data are collected and analyzed in order to explain various phenomena. Variables or features that may explain the phenomena of interest are observed, and the goal is to learn a (possibly) nonlinear function that relates the explanatory variables to phenomena of interest. To perform nonlinear function estimation, we convert a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels increase the feature set, and often result in poorly conditioned matrices. Nonetheless, we show that the matrix in our linear inverse problem contains only mild linear correlations among columns, allowing us to estimate the coefficients vector using approximate message passing (AMP), an algorithmic framework for signal reconstruction. While we model the coefficients within a Bayesian setting, which is limited in scope, AMP offers Bayes-optimal signal reconstruction quality. Numerical results confirm that our AMP-based approach learns the function better than existing approaches such as LASSO, offering markedly lower error in predicting test data.
Related Topics
Concepts
Nonlinear system
Lasso (programming language)
Algorithm
Kernel (algebra)
Applied mathematics
Bayesian probability
Inverse problem
Computer science
Function (biology)
Mathematical optimization
Polynomial kernel
Mathematics
Kernel method
Support vector machine
Artificial intelligence
World Wide Web
Mathematical analysis
Combinatorics
Evolutionary biology
Biology
Quantum mechanics
Physics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/pdf/1907.02482v1
- OA Status
- green
- References
- 28
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2953803678
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2953803678Canonical identifier for this work in OpenAlex
- Title
-
Bayesian Nonlinear Function Estimation with 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, You, Zhou, Ahmad Beirami, Dror BaronList of authors in order
- Landing page
-
https://arxiv.org/pdf/1907.02482v1Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1907.02482v1Direct OA link when available
- Concepts
-
Nonlinear system, Lasso (programming language), Algorithm, Kernel (algebra), Applied mathematics, Bayesian probability, Inverse problem, Computer science, Function (biology), Mathematical optimization, Polynomial kernel, Mathematics, Kernel method, Support vector machine, Artificial intelligence, World Wide Web, Mathematical analysis, Combinatorics, Evolutionary biology, Biology, Quantum mechanics, PhysicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
28Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.explain | 14, 22 |
| abstract_inverted_index.feature | 72 |
| abstract_inverted_index.inverse | 57, 90 |
| abstract_inverted_index.kernels | 69 |
| abstract_inverted_index.limited | 128 |
| abstract_inverted_index.massive | 3 |
| abstract_inverted_index.message | 108 |
| abstract_inverted_index.passing | 109 |
| abstract_inverted_index.perform | 49 |
| abstract_inverted_index.problem | 58, 91 |
| abstract_inverted_index.relates | 40 |
| abstract_inverted_index.results | 138 |
| abstract_inverted_index.various | 15 |
| abstract_inverted_index.Bayesian | 124 |
| abstract_inverted_index.allowing | 99 |
| abstract_inverted_index.analyzed | 10 |
| abstract_inverted_index.approach | 143 |
| abstract_inverted_index.columns, | 98 |
| abstract_inverted_index.contains | 92 |
| abstract_inverted_index.estimate | 102 |
| abstract_inverted_index.existing | 149 |
| abstract_inverted_index.features | 19 |
| abstract_inverted_index.function | 38, 51, 146 |
| abstract_inverted_index.increase | 70 |
| abstract_inverted_index.interest | 26 |
| abstract_inverted_index.markedly | 155 |
| abstract_inverted_index.offering | 154 |
| abstract_inverted_index.quality. | 136 |
| abstract_inverted_index.setting, | 125 |
| abstract_inverted_index.AMP-based | 142 |
| abstract_inverted_index.Numerical | 137 |
| abstract_inverted_index.Variables | 17 |
| abstract_inverted_index.collected | 8 |
| abstract_inverted_index.framework | 113 |
| abstract_inverted_index.interest. | 47 |
| abstract_inverted_index.matrices. | 80 |
| abstract_inverted_index.nonlinear | 37, 50, 56 |
| abstract_inverted_index.observed, | 28 |
| abstract_inverted_index.phenomena | 24, 45 |
| abstract_inverted_index.variables | 43 |
| abstract_inverted_index.(possibly) | 36 |
| abstract_inverted_index.approaches | 150 |
| abstract_inverted_index.expansion. | 67 |
| abstract_inverted_index.phenomena. | 16 |
| abstract_inverted_index.polynomial | 65 |
| abstract_inverted_index.predicting | 159 |
| abstract_inverted_index.algorithmic | 112 |
| abstract_inverted_index.approximate | 107 |
| abstract_inverted_index.conditioned | 79 |
| abstract_inverted_index.estimation, | 52 |
| abstract_inverted_index.explanatory | 42 |
| abstract_inverted_index.Nonetheless, | 81 |
| abstract_inverted_index.coefficients | 104, 121 |
| abstract_inverted_index.correlations | 96 |
| abstract_inverted_index.Bayes-optimal | 133 |
| abstract_inverted_index.reconstruction | 135 |
| abstract_inverted_index.reconstruction. | 116 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |