On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions
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.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
VEDAL: Variational Error-Driven Asynchronous Learning for 3D Gaussian Splatting Pruning
3D Gaussian Splatting (3DGS) achieves remarkable novel view synthesis quality with real-time rendering, yet suffers from excessive memory consumption due to millions of Gaussian primitives. Existing pruning methods rely …
Novel View SynthesisHow to use KL-divergence to construct conjugate priors, with well-defined non-informative limits, for the multivariate Gaussian
The Wishart distribution is the standard conjugate prior for the precision of the multivariate Gaussian likelihood, when the mean is known -- while the normal-Wishart can be used when the mean is also unknown. It is howe…
The Franz-Parisi Criterion and Computational Trade-offs in High Dimensional Statistics
Many high-dimensional statistical inference problems are believed to possess inherent computational hardness. Various frameworks have been proposed to give rigorous evidence for such hardness, including lower bounds agai…
Additive modelsPose-Free Omnidirectional Gaussian Splatting for 360-Degree Videos with Consistent Depth Priors
Omnidirectional 3D Gaussian Splatting with panoramas is a key technique for 3D scene representation, and existing methods typically rely on slow SfM to provide camera poses and sparse points priors. In this work, we prop…
Camera Pose EstimationNovel View SynthesisStructural Energy-Guided Sampling for View-Consistent Text-to-3D
Text-to-3D generation often suffers from the Janus problem, where objects look correct from the front but collapse into duplicated or distorted geometry from other angles. We attribute this failure to viewpoint bias in 2…
3D Generation