Cyclical Kernel Adaptive Metropolis

TL;DR

The paper introduces cKAM, a cyclical Kernel Adaptive Metropolis algorithm that improves exploration and avoids local trapping in sampling complex distributions, outperforming existing adaptive methods.

Contribution

cKAM incorporates a cyclical stepsize scheme to enhance exploration and escape local modes in adaptive MCMC algorithms.

Findings

cKAM effectively explores bimodal distributions.

Existing adaptive methods can fail to converge due to local trapping.

cKAM maintains high performance while escaping local modes.

Abstract

We propose cKAM, cyclical Kernel Adaptive Metropolis, which incorporates a cyclical stepsize scheme to allow control for exploration and sampling. We show that on a crafted bimodal distribution, existing Adaptive Metropolis type algorithms would fail to converge to the true posterior distribution. We point out that this is because adaptive samplers estimates the local/global covariance structure using past history of the chain, which will lead to adaptive algorithms be trapped in a local mode. We demonstrate that cKAM encourages exploration of the posterior distribution and allows the sampler to escape from a local mode, while maintaining the high performance of adaptive methods.