Nonparametric Bayesian Discrete Latent Variable Models for ...

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Bibliography D. Görür, C. E. Rasmussen, A. Tolias, F. Sinz, and N. Logothetis. Modelling spikes with mixtures of factor analysers. In C. E. Rasmussen, H. H. Buelthoff, M. A. Giese, and B. Schoelkopf, editors, Pattern Recognition, Proc. 26th DAGM Symposium, pages 391–398. Springer, 2004. D. Görür, F. Jäkel, and C. E. Rasmussen. A choice model with infinitely many latent features. In Proceedings of ICML, volume 23, 2006. J. K. Gosh and R. V. Ramamoorthi. Bayesian Nonparametrics. New York: Springer Verlag, 2003. P. Green. Reversible jump Markov chain Monte Carlo Computation and Bayesian model determination. Biometrika, 82:711–732, 1995. P. Green and S. Richardson. Modelling heterogeneity with and without the Dirichlet process. Scandinavian Journal of Statistics, 28:355–375, 2001. T. L. Griffiths and Z. Ghahramani. Infinite latent feature models and the Indian buffet process. Technical Report 2005-01, Gatsby Computational Neuroscience Unit, University College London, 2005. N. L. Hjort. Nonparametric Bayes estimators based on beta processes in models for life history data. The Annals of Statistics, 18(3):1259–1294, 1990. H. Ishwaran and L. F. James. Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96(453):161–173, March 2001. H. Ishwaran and L. F. James. Approximate Dirichlet process computing in finite normal mixtures: Smoothing and prior information. Journal of Computational and Graphical Statistics, 11(3):1–26, 2002. H. Ishwaran and L. F. James. Computational methods for multiplicative intensity models using weighted gamma processes: Proportional hazards, marked point processes, and panel count data. Journal of the American Statistical Association, 99(465):175– 190, 2004. H. Ishwaran and G. Takahara. Independent and identically distributed Monte Carlo algorithms for semiparametric linear mixed models. Journal of the American Statistical Association, 97:1154–1166, 2002. H. Ishwaran and M. Zarepour. Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models. Biometrika, 87(2):371–390, 2000. S. Jain and R. Neal. A split-merge Markov chain Monte Carlo procedure for the Dirichlet process mixture model. Journal of Computational and Graphical Statistics, 2000. S. Jain and R. M. Neal. Splitting and merging components of a nonconjugate Dirichlet process mixture model. Technical Report 0507, Department of Statistics, University of Toronto, 2005. 128
Bibliography L. F. James and J. W. Lau. Flexible choice modelling based on Bayesian nonparametric mixed multinomial logit choice models. Submitted, 2004. J. F. C. Kingman. Random discrete distributions. Journal of the Royal Statistical Society, B, 37:1–22, 1975. A. Kottas and A. E. Gelfand. Bayesian semiparametric median regression modeling,. Journal of the American Statistical Association, 96:1458–1468, 2001. K. Kurihara, M. Welling, and Y. W. Teh. Collapsed variational Dirichlet process mixture models. In Proceedings of the International Joint Conference on Artificial Intelligence, volume 20, 2007a. K. Kurihara, M. Welling, and N. Vlassis. Accelerated variational Dirichlet process mixtures. In B. Sch ´ ’olkopf, J. Platt, and T. Hofmann, editors, Advances in Neural Information Processing Systems, volume 19. MIT Press, 2007b. M. Kuss, F. Jäkel, and F. A. Wichmann. Bayesian inference for psychometric functions. Journal of Vision, 5:478–492, 2005. M. S. Lewicki. A review of methods for spike sorting: the detection and classification of neural action potentials. Network: Computation in Neural Systems, 9(4):R53–R78, 1998. J. S. Liu. Nonparametric hierarchical bayes via sequential imputations. The Annals of Statistics, 24:911–930, 1996. H. F. Lopes and M. West. Bayesian model assessment in factor analysis. Statistica Sinica, 14:41–67, 2004. R. Luce. Individual Choice Behavior. Wiley, New York, 1959. S. MacEachern and P. Müller. Efficient MCMC schemes for robust model extensions using encompassing Dirichlet process mixture models. In F. Ruggeri and D. R. Insua, editors, Robust Bayesian Analysis, pages 295–315. Springer-Verlag, 2000. S. N. MacEachern. Estimating normal means with a conjugate style Dirichlet process prior. Communications in Statistics: Simulation and Computation, 23:727–741, 1994. S. N. MacEachern and P. Müller. Estimating mixture of Dirichlet process models. Journal of Computational and Graphical Statistics, 7:223–238, 1998. S. N. MacEachern, M. Clyde, and J. S. Liu. Sequential importance sampling for nonparametric Bayes models: The next generation. The Canadian Journal of Statistics, 27(2):251–267, 1999. D. J. C. MacKay. Bayesian non-linear modeling for the energy prediction competition. ASHRAE Transactions, 100:1053–1062, 1994. 129
Page 1:
Nonparametric Bayesian Discrete Lat
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Matrizen mit unendlich vielen Spalt
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Contents Zusammenfassung iii Abstra
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List of Algorithms 1 Gibbs sampling
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Notation Matrices are capitalized a
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Symbol Meaning IBP Z binary latent
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1 Introduction belief in the prior.
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2 Nonparametric Bayesian Analysis b
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2 Nonparametric Bayesian Analysis s
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3 Dirichlet Process Mixture Models
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3.1 The Dirichlet Process the perfo
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α G o G θi x i N 3.1 The Dirichle
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15 10 5 −0.5 0 0.5 2 1 G 0 0 −0
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increment process with the correspo
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α G o π k c i θk x i 8 N 3.1 The
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3.1 The Dirichlet Process Eq. (3.21
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number of components, K number of c
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3.2 MCMC Inference in Dirichlet Pro
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and Bush and MacEachern (1996). 3.2
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3.2.2 Algorithms for non-Conjugate
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∗ π ∗ π s 3.2 MCMC Inference
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model can be written in the form of
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−1 µ y Σy Σy D ξ normal R 3.3
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the log likelihood term is: where a
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3.3 Empirical Study on the Choice o
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autocovariance coefficient 1 0.8 0.
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# of data points # of data points 5
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3.4 Dirichlet Process Mixtures of F
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µ y Σy ξ R 0 ν w normal µ −1
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ch1 ch2 ch3 ch4 3.4 Dirichlet Proce
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3.4 Dirichlet Process Mixtures of F
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# of components # of components # o
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ch 2 ch 3 ch 1 ch 2 ch 3 ch 4 3.4 D
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3.5 Discussion 3.5 Discussion In th
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4 Indian Buffet Process Models matr
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4 Indian Buffet Process Models In t
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4 Indian Buffet Process Models α z
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4 Indian Buffet Process Models α
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4 Indian Buffet Process Models The
Page 94 and 95: 4 Indian Buffet Process Models colu
Page 96 and 97: 4 Indian Buffet Process Models Pois
Page 98 and 99: 4 Indian Buffet Process Models z α
Page 100 and 101: 4 Indian Buffet Process Models For
Page 102 and 103: 4 Indian Buffet Process Models ciat
Page 104 and 105: 4 Indian Buffet Process Models rati
Page 106 and 107: 4 Indian Buffet Process Models repr
Page 108 and 109: 4 Indian Buffet Process Models samp
Page 110 and 111: 4 Indian Buffet Process Models feat
Page 112 and 113: 4 Indian Buffet Process Models Algo
Page 114 and 115: 4 Indian Buffet Process Models mixi
Page 116 and 117: 4 Indian Buffet Process Models Figu
Page 118 and 119: 4 Indian Buffet Process Models pres
Page 120 and 121: 4 Indian Buffet Process Models ε
Page 122 and 123: 4 Indian Buffet Process Models LL P
Page 124 and 125: 4 Indian Buffet Process Models P+ P
Page 126 and 127: 4 Indian Buffet Process Models tEBA
Page 128 and 129: 4 Indian Buffet Process Models dist
Page 130 and 131: 5 Conclusions has been defined as a
Page 132 and 133: A Details of Derivations for the St
Page 135 and 136: B Mathematical Appendix B.1 Dirichl
Page 137 and 138: p3 α 1 0.5 0 0 0.5 0.4 0.3 0.2 0.1
Page 139 and 140: Construction of A Process B.4 Equal
Page 141 and 142: Bibliography D. Aldous. Exchangeabi
Page 143: Bibliography T. S. Ferguson. Prior
Page 147 and 148: Bibliography R. M. Neal. Probabilis
Page 149 and 150: Bibliography Y. W. Teh, M. I. Jorda
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