Wormhole Hamiltonian Monte Carlo

By Shiwei Lan, Jeffrey Streets, Babak Shahbaba. 2013

66 citations recorded by the source corpus.

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 wormholes 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 residual energy function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Kernel Sequential Monte Carlo (2015, methodology): “In order to encourage ambiguities in the localisation task, we only use the ﬁrst 2 base sensors of [15] with known locations that each do observe distances to the S unknown sensors but not of each other.”
Boosting Variational Inference (2016, background): “[2013] and Lan et al. [2014]. We have N sensors located on a 2D plane, with coordinates θi = (xi, yi) for i = 1, · · · , N .”