# Cyclical Kernel Adaptive Metropolis

arXiv: https://arxiv.org/abs/2206.14421 · HTML: https://mlsanity.com/paper/2206.14421/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 29 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [Firefly Monte Carlo: Exact MCMC with Subsets of Data](https://mlsanity.com/paper/1403.5693/) (2014)
- [A Framework for Adaptive MCMC Targeting Multimodal Distributions](https://mlsanity.com/paper/1812.02609/) (2018)
- [Asymptotically Optimal Exact Minibatch Metropolis-Hastings](https://mlsanity.com/paper/2006.11677/) (2020)
- [AMAGOLD: Amortized Metropolis Adjustment for Efficient Stochastic Gradient MCMC](https://mlsanity.com/paper/2003.00193/) (2020)
- [Kernel Adaptive Metropolis-Hastings](https://mlsanity.com/paper/1307.5302/) (2013)
- [Accelerated dimension-independent adaptive Metropolis](https://mlsanity.com/paper/1506.05741/) (2015)
- [High-Order Stochastic Gradient Thermostats for Bayesian Learning of Deep Models](https://mlsanity.com/paper/1512.07662/) (2015)

## Abstract (arXiv)

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.