mlsanityData to 7 Oct 2026

On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions

arXiv 2209.02001 ↗First posted 5 Sep 2022math.ST cs.NA math.NAcited by 6

Not on the map. Why?

Abstract (arXiv)

We exhibit examples of high-dimensional unimodal posterior distributions arising in non-linear regression models with Gaussian process priors for which MCMC methods can take an exponential run-time to enter the regions where the bulk of the posterior measure concentrates. Our results apply to worst-case initialised (`cold start') algorithms that are local in the sense that their step-sizes cannot be too large on average. The counter-examples hold for general MCMC schemes based on gradient or random walk steps, and the theory is illustrated for Metropolis-Hastings adjusted methods such as pCN and MALA.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 25 of its 66 references that are in the map. First posted on arXiv 5 Sep 2022.

Builds on

25 of 66 references.

References · 25

  1. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  2. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  3. 2015Statistical physics of inference: Thresholds and algorithmscited by 128
  4. 2020Online stochastic gradient descent on non-convex losses from high-dimensional inferencecited by 119
  5. 2019Notes on Computational Hardness of Hypothesis Testing: Predictions using the Low-Degree Likelihood Ratiocited by 82
  6. 2014A statistical model for tensor PCAcited by 72
  7. 2020Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithmcited by 57
  8. 2015Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectorscited by 38
  9. 2015Tensor principal component analysis via sum-of-squares proofscited by 35
  10. 2022The Franz-Parisi Criterion and Computational Trade-offs in High Dimensional Statisticscited by 31
  11. 2019Passed & Spurious: Descent Algorithms and Local Minima in Spiked Matrix-Tensor Modelscited by 28
  12. 2016Statistical limits of spiked tensor modelscited by 27
13 more
  1. 2015The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Methodcited by 26
  2. 2019Who is Afraid of Big Bad Minima? Analysis of Gradient-Flow in a Spiked Matrix-Tensor Modelcited by 25
  3. 2016Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlocited by 18
  4. 2017Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squarescited by 17
  5. 2019The Kikuchi Hierarchy and Tensor PCAcited by 15
  6. 2019How to iron out rough landscapes and get optimal performances: Averaged Gradient Descent and its application to tensor PCAcited by 14
  7. 2019The Landscape of the Planted Clique Problem: Dense subgraphs and the Overlap Gap Propertycited by 9
  8. 2020Free Energy Wells and Overlap Gap Property in Sparse PCAcited by 9
  9. 2020The Boomerang Samplercited by 9
  10. 2022Almost-Linear Planted Cliques Elude the Metropolis Processcited by 7
  11. 2021Mismatching as a tool to enhance algorithmic performances of Monte Carlo methods for the planted clique modelcited by 6
  12. 2018Parallel Tempering for the planted clique problemcited by 5
  13. 2017Efficient Nonparametric Bayesian Inference For X-Ray Transformscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 1; 2026: 3.

6 papers.

  1. 2025Reasoning with Sampling: Your Base Model is Smarter Than You Thinkcited by 84
  2. 2024Improved off-policy training of diffusion samplerscited by 47
  3. 2026Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamicscited by 2
  4. 2026Fast-Mixing Markov Chains without Gradientscited by 1
  5. 2024Sampling from Boltzmann densities with physics informed low-rank formatscited by 0
  6. 2026Variational predictive resamplingcited by 0