Closed Form Variational Objectives For Bayesian Neural Networks with a Single Hidden Layer Article Swipe
In this note we consider setups in which variational objectives for Bayesian neural networks can be computed in closed form. In particular we focus on single-layer networks in which the activation function is piecewise polynomial (e.g. ReLU). In this case we show that for a Normal likelihood and structured Normal variational distributions one can compute a variational lower bound in closed form. In addition we compute the predictive mean and variance in closed form. Finally, we also show how to compute approximate lower bounds for other likelihoods (e.g. softmax classification). In experiments we show how the resulting variational objectives can help improve training and provide fast test time predictions.
Related Topics
Concepts
Softmax function
Piecewise
Artificial neural network
Focus (optics)
Bayesian probability
Polynomial
Variance (accounting)
Computer science
Mathematics
Applied mathematics
Layer (electronics)
Variational method
Upper and lower bounds
Mathematical optimization
Algorithm
Artificial intelligence
Mathematical analysis
Physics
Accounting
Chemistry
Business
Optics
Organic chemistry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1811.00686
- https://arxiv.org/pdf/1811.00686
- OA Status
- green
- Cited By
- 1
- References
- 21
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2899426887
All OpenAlex metadata
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https://openalex.org/W2899426887Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1811.00686Digital Object Identifier
- Title
-
Closed Form Variational Objectives For Bayesian Neural Networks with a Single Hidden LayerWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2018Year of publication
- Publication date
-
2018-11-02Full publication date if available
- Authors
-
Martin JankowiakList of authors in order
- Landing page
-
https://arxiv.org/abs/1811.00686Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1811.00686Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1811.00686Direct OA link when available
- Concepts
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Softmax function, Piecewise, Artificial neural network, Focus (optics), Bayesian probability, Polynomial, Variance (accounting), Computer science, Mathematics, Applied mathematics, Layer (electronics), Variational method, Upper and lower bounds, Mathematical optimization, Algorithm, Artificial intelligence, Mathematical analysis, Physics, Accounting, Chemistry, Business, Optics, Organic chemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2019: 1Per-year citation counts (last 5 years)
- References (count)
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21Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.note | 2 |
| abstract_inverted_index.show | 41, 77, 93 |
| abstract_inverted_index.test | 106 |
| abstract_inverted_index.that | 42 |
| abstract_inverted_index.this | 1, 38 |
| abstract_inverted_index.time | 107 |
| abstract_inverted_index.(e.g. | 35, 87 |
| abstract_inverted_index.bound | 58 |
| abstract_inverted_index.focus | 23 |
| abstract_inverted_index.form. | 19, 61, 73 |
| abstract_inverted_index.lower | 57, 82 |
| abstract_inverted_index.other | 85 |
| abstract_inverted_index.which | 7, 28 |
| abstract_inverted_index.Normal | 45, 49 |
| abstract_inverted_index.ReLU). | 36 |
| abstract_inverted_index.bounds | 83 |
| abstract_inverted_index.closed | 18, 60, 72 |
| abstract_inverted_index.neural | 12 |
| abstract_inverted_index.setups | 5 |
| abstract_inverted_index.compute | 54, 65, 80 |
| abstract_inverted_index.improve | 101 |
| abstract_inverted_index.provide | 104 |
| abstract_inverted_index.softmax | 88 |
| abstract_inverted_index.Bayesian | 11 |
| abstract_inverted_index.Finally, | 74 |
| abstract_inverted_index.addition | 63 |
| abstract_inverted_index.computed | 16 |
| abstract_inverted_index.consider | 4 |
| abstract_inverted_index.function | 31 |
| abstract_inverted_index.networks | 13, 26 |
| abstract_inverted_index.training | 102 |
| abstract_inverted_index.variance | 70 |
| abstract_inverted_index.piecewise | 33 |
| abstract_inverted_index.resulting | 96 |
| abstract_inverted_index.activation | 30 |
| abstract_inverted_index.likelihood | 46 |
| abstract_inverted_index.objectives | 9, 98 |
| abstract_inverted_index.particular | 21 |
| abstract_inverted_index.polynomial | 34 |
| abstract_inverted_index.predictive | 67 |
| abstract_inverted_index.structured | 48 |
| abstract_inverted_index.approximate | 81 |
| abstract_inverted_index.experiments | 91 |
| abstract_inverted_index.likelihoods | 86 |
| abstract_inverted_index.variational | 8, 50, 56, 97 |
| abstract_inverted_index.predictions. | 108 |
| abstract_inverted_index.single-layer | 25 |
| abstract_inverted_index.distributions | 51 |
| abstract_inverted_index.classification). | 89 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5054350362 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |