IEICE TRANSACTIONS on Fundamentals
Bitwise MAP Estimation for Group Testing Based on Holographic Transformation
Summary :
The main contribution of this paper is a non-trivial expression, that is called dual expression, of the posterior values for non-adaptive group testing problems. The dual expression is useful for exact bitwise MAP estimation. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-tests. If a group contains one or more positive object, the test result for the group is assumed to be one; otherwise, the test result becomes zero. Our inference problem is to evaluate the posterior probabilities of the objects from the observation of M-test results and the prior probabilities for objects. The derivation of the dual expression of posterior values can be naturally described based on a holographic transformation to the normal factor graph (NFG) representing the inference problem. In order to handle OR constraints in the NFG, we introduce a novel holographic transformation that converts an OR function to a function similar to an EQUAL function.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.12 pp.2147-2154
- Publication Date
- 2016/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.2147
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory and Techniques
Authors
Tadashi WADAYAMA
Nagoya Institute of Technology
Taisuke IZUMI
Nagoya Institute of Technology
Kazushi MIMURA
Hiroshima City University
Keyword
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Tadashi WADAYAMA, Taisuke IZUMI, Kazushi MIMURA, "Bitwise MAP Estimation for Group Testing Based on Holographic Transformation" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 12, pp. 2147-2154, December 2016, doi: 10.1587/transfun.E99.A.2147.
Abstract: The main contribution of this paper is a non-trivial expression, that is called dual expression, of the posterior values for non-adaptive group testing problems. The dual expression is useful for exact bitwise MAP estimation. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-tests. If a group contains one or more positive object, the test result for the group is assumed to be one; otherwise, the test result becomes zero. Our inference problem is to evaluate the posterior probabilities of the objects from the observation of M-test results and the prior probabilities for objects. The derivation of the dual expression of posterior values can be naturally described based on a holographic transformation to the normal factor graph (NFG) representing the inference problem. In order to handle OR constraints in the NFG, we introduce a novel holographic transformation that converts an OR function to a function similar to an EQUAL function.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.2147/_p
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@ARTICLE{e99-a_12_2147,
author={Tadashi WADAYAMA, Taisuke IZUMI, Kazushi MIMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Bitwise MAP Estimation for Group Testing Based on Holographic Transformation},
year={2016},
volume={E99-A},
number={12},
pages={2147-2154},
abstract={The main contribution of this paper is a non-trivial expression, that is called dual expression, of the posterior values for non-adaptive group testing problems. The dual expression is useful for exact bitwise MAP estimation. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-tests. If a group contains one or more positive object, the test result for the group is assumed to be one; otherwise, the test result becomes zero. Our inference problem is to evaluate the posterior probabilities of the objects from the observation of M-test results and the prior probabilities for objects. The derivation of the dual expression of posterior values can be naturally described based on a holographic transformation to the normal factor graph (NFG) representing the inference problem. In order to handle OR constraints in the NFG, we introduce a novel holographic transformation that converts an OR function to a function similar to an EQUAL function.},
keywords={},
doi={10.1587/transfun.E99.A.2147},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Bitwise MAP Estimation for Group Testing Based on Holographic Transformation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2147
EP - 2154
AU - Tadashi WADAYAMA
AU - Taisuke IZUMI
AU - Kazushi MIMURA
PY - 2016
DO - 10.1587/transfun.E99.A.2147
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2016
AB - The main contribution of this paper is a non-trivial expression, that is called dual expression, of the posterior values for non-adaptive group testing problems. The dual expression is useful for exact bitwise MAP estimation. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-tests. If a group contains one or more positive object, the test result for the group is assumed to be one; otherwise, the test result becomes zero. Our inference problem is to evaluate the posterior probabilities of the objects from the observation of M-test results and the prior probabilities for objects. The derivation of the dual expression of posterior values can be naturally described based on a holographic transformation to the normal factor graph (NFG) representing the inference problem. In order to handle OR constraints in the NFG, we introduce a novel holographic transformation that converts an OR function to a function similar to an EQUAL function.
ER -
English
