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Asymptotically Exact Data Augmentation: Models, Properties, and Algorithms

Abstract : Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo ones. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution and offering a computationally efficient inference cannot be conducted in a systematic way. To deal with such issues, this article studies a unified framework, coined asymptotically exact data augmentation (AXDA), which encompasses both well-established and more recent approximate augmented models. In a broader perspective, this article shows that AXDA models can benefit from interesting statistical properties and yield efficient inference algorithms. In non-asymptotic settings, the quality of the proposed approximation is assessed with several theoretical results. The latter are illustrated on standard statistical problems.
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https://hal.archives-ouvertes.fr/hal-03064884
Contributor : Nicolas Dobigeon <>
Submitted on : Monday, December 14, 2020 - 3:54:49 PM
Last modification on : Thursday, March 18, 2021 - 2:16:16 PM

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Maxime Vono, Nicolas Dobigeon, Pierre Chainais. Asymptotically Exact Data Augmentation: Models, Properties, and Algorithms. Journal of Computational and Graphical Statistics, Taylor & Francis, 2020, pp.1-14. ⟨10.1080/10618600.2020.1826954⟩. ⟨hal-03064884⟩

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