Continuous Herded Gibbs Sampling
This work addresses the computational bottleneck in sampling for high-dimensional densities, offering a more efficient deterministic method, though it appears incremental as it builds on existing herding and Gibbs sampling techniques.
The paper tackled the problem of generating deterministic samples from high-dimensional multivariate probability densities by proposing a continuous herded Gibbs sampler, which reduces L2 error similarly to kernel herding while achieving significantly lower computation time that scales linearly with dimensions.
Herding is a technique to sequentially generate deterministic samples from a probability distribution. In this work, we propose a continuous herded Gibbs sampler that combines kernel herding on continuous densities with the Gibbs sampling idea. Our algorithm allows for deterministically sampling from high-dimensional multivariate probability densities, without directly sampling from the joint density. Experiments with Gaussian mixture densities indicate that the L2 error decreases similarly to kernel herding, while the computation time is significantly lower, i.e., linear in the number of dimensions.