TY - GEN
T1 - Wormhole Hamiltonian Monte Carlo
AU - Lan, Shiwei
AU - Streets, Jeffrey
AU - Shahbaba, Babak
N1 - Publisher Copyright:
Copyright © 2014, Association for the Advancement of Artificial Intelligence.
PY - 2014
Y1 - 2014
N2 - 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 rediscovering 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.
AB - 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 rediscovering 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.
UR - http://www.scopus.com/inward/record.url?scp=84908213959&partnerID=8YFLogxK
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M3 - Conference contribution
AN - SCOPUS:84908213959
T3 - Proceedings of the National Conference on Artificial Intelligence
SP - 1953
EP - 1959
BT - Proceedings of the National Conference on Artificial Intelligence
PB - AI Access Foundation
T2 - 28th AAAI Conference on Artificial Intelligence, AAAI 2014, 26th Innovative Applications of Artificial Intelligence Conference, IAAI 2014 and the 5th Symposium on Educational Advances in Artificial Intelligence, EAAI 2014
Y2 - 27 July 2014 through 31 July 2014
ER -