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Insights Into Multiple/Single Lower Bound Approximation for Extended Variational Inference in Non-Gaussian Structured Data Modeling

Ma, Z; Xie, J; Lai, Y; Taghia, J; Xue, J-H; Guo, J; (2019) Insights Into Multiple/Single Lower Bound Approximation for Extended Variational Inference in Non-Gaussian Structured Data Modeling. IEEE Transactions on Neural Networks and Learning Systems 10.1109/tnnls.2019.2899613. Green open access

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Abstract

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.

Type: Article
Title: Insights Into Multiple/Single Lower Bound Approximation for Extended Variational Inference in Non-Gaussian Structured Data Modeling
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/tnnls.2019.2899613
Publisher version: https://doi.org/10.1109/TNNLS.2019.2899613
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Structured data, Beyesian estimation, nonGaussian statistical models, extended variational inference, lowerbound approximation
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10078215
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