mlsanityData to 7 Oct 2026

Bayes Hilbert Spaces for Posterior Approximation

arXiv 2304.09053 ↗First posted 18 Apr 2023math.ST stat.ME stat.MLcited by 1

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Abstract (arXiv)

Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to evaluate is a popular approach to circumvent this issue. This begs the question of what is an appropriate space to perform approximation of Bayesian posterior measures. This manuscript studies the application of Bayes Hilbert spaces to the posterior approximation problem. Bayes Hilbert spaces are studied in functional data analysis in the context where observed functions are probability density functions and their application to computational Bayesian problems is in its infancy. This manuscript shall outline Bayes Hilbert spaces and their connection to Bayesian computation, in particular novel connections between Bayes Hilbert spaces, Bayesian coreset algorithms and kernel-based distances.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 26 of its 75 references that are in the map. First posted on arXiv 18 Apr 2023.

Builds on

26 of 75 references.

References · 26

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14 more
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  1. 2025On Reconstructing Training Data From Bayesian Posteriors and Trained Modelscited by 0