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  Geometric variational inference

Frank, P., Leike, R., & Ensslin, T. A. (2021). Geometric variational inference. Entropy, 23(7): 853. doi:10.3390/e23070853.

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 Creators:
Frank, Philipp1, Author              
Leike, Reimar2, Author              
Ensslin, Torsten A.1, Author              
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1Computational Structure Formation, MPI for Astrophysics, Max Planck Society, ou_2205642              
2Physical Cosmology, MPI for Astrophysics, Max Planck Society, ou_2205644              

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 Abstract: Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions.

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Language(s): eng - English
 Dates: 2021-07-02
 Publication Status: Published online
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 Rev. Type: Peer
 Identifiers: DOI: 10.3390/e23070853
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Title: Entropy
Source Genre: Journal
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Publ. Info: Basel : Molecular Diversity Preservation International
Pages: - Volume / Issue: 23 (7) Sequence Number: 853 Start / End Page: - Identifier: ISSN: 1099-4300
CoNE: https://pure.mpg.de/cone/journals/resource/110978984445793