Research map / Probabilistic and scientific modeling / Variational and generative sampling
Beyond Log-concavity: Provable Guarantees for Sampling Multi-modal Distributions using Simulated Tempering Langevin Monte Carlo
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use simulated tempering to move between temperatures while running Langevin dynamics | Langevin Monte Carlo for equal-variance Gaussian mixtures · Equal-variance Gaussian mixtures | TV distance: at most ε | Helped |
| Allow bounded function and gradient perturbations from an equal-variance Gaussian mixture | Simulated Tempering Langevin Monte Carlo · Perturbed equal-variance Gaussian mixtures | TV distance: ≤ ε | Helped |
| Use local Langevin steps without tempering | Sampling well-separated multimodal distributions · Well-separated Gaussian mixture modes | mixing | Hurt |
| Allow mixture components to have different covariance | Simulated tempering for Gaussian mixtures · Gaussian mixtures with unequal covariance | mixing time: factor of 2 | Hurt |
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