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New MCMC methods offer rotation-invariant sampling for manifold-valued data

By PulseAugur Editorial · [4 sources] ·

Researchers have developed novel methods for Markov chain Monte Carlo (MCMC) sampling, focusing on improving efficiency and robustness. One approach introduces an intrinsic effective sample size metric based on kernel discrepancy, designed to be invariant to coordinate system changes for manifold-valued samples. Another method, APM-SGHMC, uses adaptive principal component transformations to create rotation-invariant samplers for Bayesian structural system identification, demonstrating zero-shot generalization across diverse tasks without retraining. AI

IMPACT These advancements in MCMC sampling could enhance the efficiency and reliability of complex Bayesian inference tasks, potentially impacting fields that rely on probabilistic modeling.

RANK_REASON The cluster contains two arXiv papers detailing new methodologies in MCMC sampling.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 4 sources. How we write summaries →

New MCMC methods offer rotation-invariant sampling for manifold-valued data

COVERAGE [4]

  1. arXiv cs.LG TIER_1 English(EN) · Kisung You ·

    Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy

    arXiv:2605.03266v1 Announce Type: cross Abstract: Effective sample size is a standard summary of Markov chain Monte Carlo output, but it is usually attached to scalar or Euclidean summaries chosen by the analyst. For manifold-valued samples this choice is not canonical: coordinat…

  2. arXiv stat.ML TIER_1 English(EN) · Kisung You ·

    Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy

    Effective sample size is a standard summary of Markov chain Monte Carlo output, but it is usually attached to scalar or Euclidean summaries chosen by the analyst. For manifold-valued samples this choice is not canonical: coordinate-wise effective sample sizes can change under rot…

  3. arXiv stat.ML TIER_1 English(EN) · Xianghao Meng, Yong Huang, James L. Beck, Kui Jiang, Hui Li ·

    MCMC with Adaptive Principal-Component Transformation: Rotation-Invariant Universal Samplers for Bayesian Structural System Identification

    arXiv:2604.23381v1 Announce Type: cross Abstract: Over decades, Markov chain Monte Carlo (MCMC) methods have been widely studied, with a typical application being the quantification of posterior uncertainties in Bayesian system identification of structural dynamic models. To addr…

  4. arXiv stat.ML TIER_1 English(EN) · Hui Li ·

    MCMC with Adaptive Principal-Component Transformation: Rotation-Invariant Universal Samplers for Bayesian Structural System Identification

    Over decades, Markov chain Monte Carlo (MCMC) methods have been widely studied, with a typical application being the quantification of posterior uncertainties in Bayesian system identification of structural dynamic models. To address the issue of excessively low sampling efficien…

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