- Shiwei Lan: Department of Statistics University of California, Irvine.
- Jeffrey Streets: Department of Mathematics University of California, Irvine.
- Babak Shahbaba: Department of Statistics University of California, Irvine.
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to redis-covering those previously identified, we employ a novel mode searching algorithm that explores a function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function.