Abhijoy Saha
A geometric variational approach to Bayesian inference
Saha, Abhijoy; Bharath, Karthik; Kurtek, Sebastian
Abstract
We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher–Rao metric on the manifold of probability density functions. Under the square-root density representation, the manifold can be identified with the positive orthant of the unit hypersphere S ∞ in L 2 , and the Fisher–Rao metric reduces to the standard L 2 metric. Exploiting such a Riemannian structure, we formulate the task of approximating the posterior distribution as a variational problem on the hypersphere based on the α-divergence. This provides a tighter lower bound on the marginal distribution when compared to, and a corresponding upper bound unavailable with, approaches based on the Kullback–Leibler divergence. We propose a novel gradient-based algorithm for the variational problem based on Fréchet derivative operators motivated by the geometry of S ∞ , and examine its properties. Through simulations and real data applications, we demonstrate the utility of the proposed geometric framework and algorithm on several Bayesian models.
Citation
Saha, A., Bharath, K., & Kurtek, S. (2020). A geometric variational approach to Bayesian inference. Journal of the American Statistical Association, 115(530), 822-835. https://doi.org/10.1080/01621459.2019.1585253
Journal Article Type | Article |
---|---|
Acceptance Date | Jan 30, 2019 |
Online Publication Date | Mar 26, 2019 |
Publication Date | 2020 |
Deposit Date | Mar 8, 2019 |
Publicly Available Date | Mar 29, 2024 |
Journal | Journal of the American Statistical Association |
Print ISSN | 0162-1459 |
Electronic ISSN | 1537-274X |
Publisher | Taylor and Francis |
Peer Reviewed | Peer Reviewed |
Volume | 115 |
Issue | 530 |
Pages | 822-835 |
DOI | https://doi.org/10.1080/01621459.2019.1585253 |
Keywords | Infinite-dimensional Riemannian optimization; Gradient ascent algorithm; Square- root density; Bayesian density estimation; Bayesian logistic regression |
Public URL | https://nottingham-repository.worktribe.com/output/1620463 |
Publisher URL | https://www.tandfonline.com/doi/full/10.1080/01621459.2019.1585253 |
Additional Information | This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 26.03.2019 , available online: http://www.tandfonline.com/10.1080/01621459.2019.1585253 |
Files
A Geometric Variational Approach to Bayesian Inference
(3.8 Mb)
PDF
You might also like
Shape and Structure Preserving Differential Privacy
(2022)
Presentation / Conference
Variograms for kriging and clustering of spatial functional data with phase variation
(2022)
Journal Article
Differential privacy over Riemannian manifolds
(2021)
Conference Proceeding
Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology
(2021)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: digital-library-support@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search