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Insights Into Multi...
Insights Into Multiple/Single Lower Bound Approximation for Extended Variational Inference in Non-Gaussian Structured Data Modeling
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- Ma, Zhanyu (författare)
- Beijing Univ Posts & Telecommun, Pattern Recognit & Intelligent Syst Lab, Beijing 100876, Peoples R China.
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- Xie, Jiyang (författare)
- Beijing Univ Posts & Telecommun, Pattern Recognit & Intelligent Syst Lab, Beijing 100876, Peoples R China.
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- Lai, Yuping (författare)
- North China Univ Technol, Dept Informat Secur, Beijing 100144, Peoples R China.
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- Taghia, Jalil (författare)
- Uppsala universitet,Avdelningen för systemteknik
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- Xue, Jing-Hao (författare)
- UCL, Dept Stat Sci, London WC1E 6BT, England.
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- Guo, Jun (författare)
- Beijing Univ Posts & Telecommun, Pattern Recognit & Intelligent Syst Lab, Beijing 100876, Peoples R China.
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Beijing Univ Posts & Telecommun, Pattern Recognit & Intelligent Syst Lab, Beijing 100876, Peoples R China North China Univ Technol, Dept Informat Secur, Beijing 100144, Peoples R China. (creator_code:org_t)
- 2020
- 2020
- Engelska.
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Ingår i: IEEE Transactions on Neural Networks and Learning Systems. - 2162-237X .- 2162-2388. ; 31:7, s. 2240-2254
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- For most of the non-Gaussian statistical models, the data being modeled represent strongly structured properties, such as scalar data with bounded support (e.g., beta distribution), vector data with unit length (e.g., Dirichlet distribution), and vector data with positive elements (e.g., generalized inverted Dirichlet distribution). In practical implementations of non-Gaussian statistical models, it is infeasible to find an analytically tractable solution to estimating the posterior distributions of the parameters. Variational inference (VI) is a widely used framework in Bayesian estimation. Recently, an improved framework, namely, the extended VI (EVI), has been introduced and applied successfully to a number of non-Gaussian statistical models. EVI derives analytically tractable solutions by introducing lower bound approximations to the variational objective function. In this paper, we compare two approximation strategies, namely, the multiple lower bounds (MLBs) approximation and the single lower bound (SLB) approximation, which can be applied to carry out the EVI. For implementation, two different conditions, the weak and the strong conditions, are discussed. Convergence of the EVI depends on the selection of the lower bound, regardless of the choice of weak or strong condition. We also discuss the convergence properties to clarify the differences between MLB and SLB. Extensive comparisons are made based on some EVI-based non-Gaussian statistical models. Theoretical analysis is conducted to demonstrate the differences between the weak and strong conditions. Experimental results based on real data show advantages of the SLB approximation over the MLB approximation.
Ämnesord
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
Nyckelord
- Bayes methods
- Linear programming
- Convergence
- Computational modeling
- Data models
- Maximum likelihood estimation
- Beyesian estimation
- extended variational inference (EVI)
- lower bound approximation
- non-Gaussian statistical models
- structured data
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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