Research map / Probabilistic and scientific modeling / Variational and generative sampling
Fast Conditional Mixing of MCMC Algorithms for Non-log-concave Distributions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Analyze LMC convergence conditioned on each mixture component region, using its local LSI | Langevin Monte Carlo on Gaussian mixtures with uniform covariance · Gaussian mixtures with uniform covariance (ν1 and ν3) | conditional KL divergence | Helped |
| Analyze convergence conditioned on a local region rather than requiring global convergence | Langevin Monte Carlo · Gaussian mixtures (ν1 and ν3) | global KL divergence | Mixed |
| Use conditional rather than global convergence analysis | Langevin Monte Carlo on dense Gaussian mixtures · ν2 | KL divergence | Helped |
| Analyze Gibbs sampling conditioned on a subset with a spectral gap lower bound | Gibbs sampling on finite states · Finite-state Gibbs sampling on the hypercube | conditional chi-squared divergence: 1/(α√T) | Helped |
| Require a quasi-convex subset with a well-connected local minimum | Conditional Gibbs sampler · Quasi-convex subset of the hypercube | spectral gap: 1/(16d^2D^2) | Helped |
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