Black-box importance sampling

Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017

Volumn , Issue , 2017, Pages

  Liu, Qiang ^a   Lee, Jason D ^b  

^a DARTMOUTH COLLEGE   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; SAMPLING;

BLACK BOXES; EMPIRICAL ANALYSIS; IMPORTANCE SAMPLING METHOD; IMPORTANCE WEIGHTS;

IMPORTANCE SAMPLING;

EID: 85083938188     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (49)

1. Pierre Alquier, Nial Friel, Richard Everitt, and Aidan Boland. Noisy Monte Carlo: Convergence of markov chains with approximate transition kernels. Statistics and Computing, 26(1-2):29–47, 2016.
2. Francis Bach. On the equivalence between quadrature rules and random features. arXiv preprint arXiv:1502.06800, 2015.
3. K. Bache and M. Lichman. UCI machine learning repository, 2013. URL http://archive.ics.uci.edu/ml.
4. Frederik Beaujean and Allen Caldwell. Initializing adaptive importance sampling with markov chains. arXiv preprint arXiv:1304.7808, 2013.
5. Zdravko I Botev, Pierre L’Ecuyer, and Bruno Tuffin. Markov chain importance sampling with applications to rare event probability estimation. Statistics and Computing, 23(2):271–285, 2013.
6. Leo Breiman. Better subset regression using the nonnegative garrote. Technometrics, 37(4):373–384, 1995.
7. François-Xavier Briol, Chris Oates, Mark Girolami, and Michael A Osborne. Frank-Wolfe Bayesian Quadrature: Probabilistic integration with theoretical guarantees. In NIPS, 2015a.
8. François-Xavier Briol, Chris Oates, Mark Girolami, Michael A Osborne, Dino Sejdinovic, et al. Probabilistic integration: A role for statisticians in numerical analysis? arXiv preprint http://arxiv.org/abs/1512.00933, 2015b.
9. Yutian Chen, Max Welling, and Alex Smola. Super-samples from kernel herding. In UAI, 2010.
10. Kacper Chwialkowski, Heiko Strathmann, and Arthur Gretton. A kernel test of goodness of fit. In ICML, 2016.
11. Ronan Collobert, Samy Bengio, and Yoshua Bengio. A parallel mixture of SVMs for very large scale problems. Neural computation, 14(5):1105–1114, 2002.
12. Bernard Delyon and François Portier. Integral approximation by kernel smoothing. arXiv preprint arXiv:1409.0733, 2014.
13. Bradley Efron. Bayesian inference and the parametric bootstrap. The annals of applied statistics, 6(4):1971, 2012.
14. Zoubin Ghahramani and Carl E Rasmussen. Bayesian Monte Carlo. In NIPS, 2002.
15. Evan Greensmith, Peter L Bartlett, and Jonathan Baxter. Variance reduction techniques for gradient estimates in reinforcement learning. Journal of Machine Learning Research, 5(Nov):1471–1530, 2004.
16. Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola. A kernel two-sample test. The Journal of Machine Learning Research, 13(1):723–773, 2012.
17. Tamir Hazan, Subhransu Maji, and Tommi Jaakkola. On sampling from the gibbs distribution with random maximum a-posteriori perturbations. In NIPS, pages 1268–1276, 2013.
18. Masayuki Henmi, Ryo Yoshida, and Shinto Eguchi. Importance sampling via the estimated sampler. Biometrika, 94(4):985–991, 2007.
19. Matthew D Hoffman and Andrew Gelman. The no-u-turn sampler: adaptively setting path lengths in hamiltonian monte carlo. Journal of Machine Learning Research, 15 (1):1593–1623, 2014.
20. Ferenc Huszár and David Duvenaud. Optimally-weighted Herding is Bayesian quadrature. In UAI, 2012.
21. Lihong Li, Rémi Munos, and Csaba Szepesvári. Toward minimax off-policy value estimation. In AISTATS, 2015.
22. Jun S Liu. Monte Carlo strategies in scientific computing. Springer Science & Business Media, 2008.
23. Qiang Liu, John W Fisher III, and Alexander T Ihler. Probabilistic variational bounds for graphical models. In NIPS, pages 1432–1440, 2015.
24. Qiang Liu, Jason D Lee, and Michael I Jordan. A kernelized stein discrepancy for goodness-of-fit tests and model evaluation. In ICML, 2016.
25. Steven N MacEachern, Merlise Clyde, and Jun S Liu. Sequential importance sampling for nonparametric Bayes models: The next generation. Canadian Journal of Statistics, 27(2):251–267, 1999.
26. Luca Martino, Victor Elvira, David Luengo, and Jukka Corander. Layered adaptive importance sampling. Statistics and Computing, pages 1–25.
27. RD Morris, X Descombes, and J Zerubia. The Ising/Potts model is not well suited to segmentation tasks. In Digital Signal Processing Workshop Proceedings, 1996., IEEE, pages 263–266. IEEE, 1996.
28. Radford M Neal. Annealed importance sampling. Statistics and Computing, 11(2):125–139, 2001.
29. Barry L Nelson. On control variate estimators. Computers & Operations Research, 14(3):219–225, 1987.
30. XuanLong Nguyen, Martin J Wainwright, Michael Jordan, et al. Estimating divergence functionals and the likelihood ratio by convex risk minimization. Information Theory, IEEE Transactions on, 56(11):5847–5861, 2010.
31. Harald Niederreiter. Quasi-Monte Carlo Methods. Wiley Online Library, 2010.
32. Chris J Oates, Jon Cockayne, François-Xavier Briol, and Mark Girolami. Convergence rates for a class of estimators based on stein’s identity. arXiv preprint arXiv:1603.03220, 2016.
33. Chris J Oates, Mark Girolami, and Nicolas Chopin. Control functionals for Monte Carlo integration. Journal of the Royal Statistical Society, Series B, 2017.
34. Anthony O’Hagan. Monte carlo is fundamentally unsound. Journal of the Royal Statistical Society. Series D (The Statistician), 36(2/3):247–249, 1987.
35. Anthony O’Hagan. Bayes–Hermite quadrature. Journal of statistical planning and inference, 29(3):245–260, 1991.
36. George Papandreou and Alan L Yuille. Perturb-and-map random fields: Using discrete optimization to learn and sample from energy models. In ICCV, pages 193–200. IEEE, 2011.
37. Rajesh Ranganath, Sean Gerrish, and David M Blei. Black box variational inference. In AISTATS, pages 814–822, 2014.
38. Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. In ICML, 2015.
39. Christian Robert and George Casella. Monte Carlo statistical methods. Springer Science & Business Media, 2013.
40. Tim Salimans, Diederik P Kingma, and Max Welling. Markov chain Monte Carlo and variational inference: Bridging the gap. In ICML, 2015.
41. Adrian Smith, Arnaud Doucet, Nando de Freitas, and Neil Gordon. Sequential Monte Carlo Methods in Practice. Springer Science & Business Media, 2013.
42. Masashi Sugiyama and Motoaki Kawanabe. Machine learning in non-stationary environments: Introduction to covariate shift adaptation. MIT Press, 2012.
43. Masashi Sugiyama, Shinichi Nakajima, Hisashi Kashima, Paul V Buenau, and Motoaki Kawanabe. Direct importance estimation with model selection and its application to covariate shift adaptation. In NIPS, 2008.
44. Yee Whye Teh, Alexandre H Thiery, and Sebastian J Vollmer. Consistency and fluctuations for stochastic gradient langevin dynamics. Journal of Machine Learning Research, 17, 2016.
45. Martin J Wainwright and Michael I Jordan. Graphical models, exponential families, and variational inference. Foundations and TrendsR in Machine Learning, 1(1-2): 1–305, 2008.
46. Chong Wang, Xi Chen, Alex J Smola, and Eric P Xing. Variance reduction for stochastic gradient optimization. In Advances in Neural Information Processing Systems, pages 181–189, 2013.
47. Max Welling and Yee W Teh. Bayesian learning via stochastic gradient Langevin dynamics. In ICML, 2011.
48. Xiukai Yuan, Zhenzhou Lu, Changcong Zhou, and Zhufeng Yue. A novel adaptive importance sampling algorithm based on markov chain and low-discrepancy sequence. Aerospace Science and Technology, 29(1):253–261, 2013.
49. Peilin Zhao and Tong Zhang. Stochastic optimization with importance sampling. ICML, 2015.