On the convergence of stochastic gradient MCMC algorithms with high-order integrators

Advances in Neural Information Processing Systems

Volumn 2015-January, Issue , 2015, Pages 2278-2286

  Chen, Changyou ^a   Ding, Nan ^b   Carin, Lawrence ^a  

^a Duke University   (United States)

^b GOOGLE INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; INFORMATION SCIENCE; MEAN SQUARE ERROR;

CONVERGENCE RATES; CONVERGENCE RESULTS; FASTER CONVERGENCE; FINITE-TIME CONVERGENCE; OPTIMAL CONVERGENCE; REAL APPLICATIONS; STOCHASTIC GRADIENT; SYMMETRIC SPLITTING;

STOCHASTIC SYSTEMS;

EID: 84965095225     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. T. Chen, E. B. Fox, and C. Guestrin. Stochastic gradient Hamiltonian Monte Carlo. In ICML, 2014.
2. N. Ding, Y. Fang, R. Babbush, C. Chen, R. D. Skeel, and H. Neven. Bayesian sampling using stochastic gradient thermostats. In NIPS, 2014.
3. H. Risken. The Fokker-Planck equation. Springer-Verlag, New York, 1989.
4. M. Welling and Y. W. Teh. Bayesian learning via stochastic gradient Langevin dynamics. In ICML, 2011.
5. Y. W. Teh, A. H. Thiery, and S. J. Vollmer. Consistency and fluctuations for stochastic gradient Langevin dynamics. Technical Report arXiv:1409.0578, University of Oxford, UK, Sep. 2014. URL http://arxiv.org/abs/1409.0578.
6. S. J. Vollmer, K. C. Zygalakis, and Y. W. Teh. (Non-) asymptotic properties of stochastic gradient Langevin dynamics. Technical Report arXiv:1501.00438, University of Oxford, UK, January 2015. URL http://arxiv.org/abs/1501.00438.
7. M. Betancourt. The fundamental incompatibility of Hamiltonian Monte Carlo and data subsampling. In ICML, 2015.
8. I. Sato and H. Nakagawa. Approximation analysis of stochastic gradient Langevin dynamics by using Fokker-Planck equation and Itõ process. In ICML, 2014.
9. B. Leimkuhler and X. Shang. Adaptive thermostats for noisy gradient systems. Technical Report arXiv:1505.06889v1, University of Edinburgh, UK, May 2015. URL http://arxiv.org/abs/1505.06889.
10. A. Abdulle, G. Vilmart, and K. C. Zygalakis. Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. SIAM J. NUMER. ANAL., 53(1):1-16, 2015.
11. R. Hasminskii. Stochastic stability of differential equations. Springer-Verlag Berlin Heidelberg, 2012.
12. J. C. Mattingly, A. M. Stuart, and M. V. Tretyakov. Construction of numerical time-average and stationary measures via Poisson equations. SIAM J. NUMER. ANAL., 48(2):552-577, 2010.
13. P. Giesl. Construction of global Lyapunov functions using radial basis functions. Springer Berlin Heidelberg, 2007.
14. N. N. Bogoliubov and N. M. Krylov. La theorie generalie de la mesure dans son application a l'etude de systemes dynamiques de la mecanique non-lineaire. Ann. Math. II (in French), 38(1):65-113, 1937.
15. B. Leimkuhler and C. Matthews. Rational construction of stochastic numerical methods for molecular sampling. AMRX, 2013(1):34-56, 2013.
16. D. M. Blei, A. Y. Ng, and M. I. Jordan. Latent Dirichlet allocation. JMLR, 2003.
17. M. D. Hoffman, D. M. Blei, and F. Bach. Online learning for latent Dirichlet allocation. In NIPS, 2010.
18. Z. Gan, C. Chen, R. Henao, D. Carlson, and L. Carin. Scalable deep Poisson factor analysis for topic modeling. In ICML, 2015.
19. S. Patterson and Y. W. Teh. Stochastic gradient Riemannian Langevin dynamics on the probability simplex. In NIPS, 2013.
20. Z. Gan, R. Henao, D. Carlson, and L. Carin. Learning deep sigmoid belief networks with data augmentation. In AISTATS, 2015.
21. R. Salakhutdinov and I. Murray. On the quantitative analysis of deep belief networks. In ICML, 2008.
22. A. Mnih and K. Gregor. Neural variational inference and learning in belief networks. In ICML, 2014.
23. A. Debussche and E. Faou. Weak backward error analysis for SDEs. SIAM J. NUMER. ANAL., 50(3):1734-1752, 2012.
24. M. Kopec. Weak backward error analysis for overdamped Langevin processes. IMA J. NUMER. ANAL., 2014.