mlsanityData to 7 Oct 2026

Semiparametric inference using fractional posteriors

arXiv 2301.08158 ↗First posted 19 Jan 2023math.ST stat.ML stat.THcited by 4

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Abstract (arXiv)

We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for different classes of prior distributions, including Gaussian process priors. We show that fractional posterior credible sets can provide reliable semiparametric uncertainty quantification, but have inflated size. To remedy this, we further propose a textitshifted-and-rescaled fractional posterior set that is an efficient confidence set having optimal size under regularity conditions. As part of our proofs, we also refine existing contraction rate results for fractional posteriors by sharpening the dependence of the rate on the fractional exponent.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 16 of its 55 references that are in the map. First posted on arXiv 19 Jan 2023.

Builds on

16 of 55 references.

References · 16

  1. 2018Understanding disentangling in β-VAEcited by 332
  2. 2021User-friendly introduction to PAC-Bayes boundscited by 234
  3. 2013A General Framework for Updating Belief Distributionscited by 172
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  5. 2014Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing Itcited by 92
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  12. 2018Improving Explorability in Variational Inference with Annealed Variational Objectivescited by 24
4 more
  1. 2020A comparison of learning rate selection methods in generalized Bayesian inferencecited by 23
  2. 2021On the Robustness to Misspecification of α-Posteriors and Their Variational Approximationscited by 15
  3. 2019Empirical priors for prediction in sparse high-dimensional linear regressioncited by 6
  4. 2017An asymptotic analysis of distributed nonparametric methodscited by 5

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Cited by year

Citing papers per year: 2024: 4.

4 papers.

  1. 2024Posterior and variational inference for deep neural networks with heavy-tailed weightscited by 9
  2. 2024Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrixcited by 8
  3. 2024Deep Horseshoe Gaussian Processescited by 5
  4. 2024Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variancecited by 1