Nonparametric Bayesian Discrete Latent Variable Models for ...

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3 Dirichlet Process Mixture Models Table 3.2: Paired t-test scores of leave one out predictive densities. The test does not give enough evidence in case of the Geyser data, however it shows that KDE is statistically significantly different than both DP models for the higher dimensional data sets. Also, CDP is signifcantly different than CCDP for the Wine data. 400 300 200 100 0 600 500 400 300 200 100 0 Data set KDE/CDP KDE/CCDP CDP/CCDP Geyser 0.95 0.59 0.41 Spiral
# of data points # of data points 50 40 30 20 10 60 50 40 30 20 10 geyser 0 0 5 10 15 components iris 0 0 5 10 15 components 3.3 Empirical Study on the Choice of the Base Distribution # of data points # of data points 80 70 60 50 40 30 20 10 0 70 60 50 40 30 20 10 spirals 0 5 10 15 20 25 components wine 0 0 5 10 15 components Figure 3.15: Number of data points assigned to the components averaged over different positions in the chain. The standard deviations are indicated by the error bars. Note the existence of many small components for the CCDP model CDP CCDP 51
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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
Page 15: Symbol Meaning IBP Z binary latent
Page 18 and 19: 1 Introduction belief in the prior.
Page 20 and 21: 2 Nonparametric Bayesian Analysis b
Page 22 and 23: 2 Nonparametric Bayesian Analysis s
Page 25 and 26: 3 Dirichlet Process Mixture Models
Page 27 and 28: 3.1 The Dirichlet Process the perfo
Page 29 and 30: α G o G θi x i N 3.1 The Dirichle
Page 31 and 32: 15 10 5 −0.5 0 0.5 2 1 G 0 0 −0
Page 33 and 34: increment process with the correspo
Page 35 and 36: α G o π k c i θk x i 8 N 3.1 The
Page 37 and 38: 3.1 The Dirichlet Process Eq. (3.21
Page 39 and 40: number of components, K number of c
Page 41 and 42: 3.2 MCMC Inference in Dirichlet Pro
Page 43 and 44: and Bush and MacEachern (1996). 3.2
Page 45 and 46: 3.2.2 Algorithms for non-Conjugate
Page 55 and 56: ∗ π ∗ π s 3.2 MCMC Inference
Page 57 and 58: model can be written in the form of
Page 59 and 60: −1 µ y Σy Σy D ξ normal R 3.3
Page 61 and 62: the log likelihood term is: where a
Page 63 and 64: 3.3 Empirical Study on the Choice o
Page 65: autocovariance coefficient 1 0.8 0.
Page 69 and 70: 3.4 Dirichlet Process Mixtures of F
Page 71 and 72: µ y Σy ξ R 0 ν w normal µ −1
Page 73 and 74: ch1 ch2 ch3 ch4 3.4 Dirichlet Proce
Page 75 and 76: 3.4 Dirichlet Process Mixtures of F
Page 77 and 78: # of components # of components # o
Page 79 and 80: ch 2 ch 3 ch 1 ch 2 ch 3 ch 4 3.4 D
Page 81: 3.5 Discussion 3.5 Discussion In th
Page 84 and 85: 4 Indian Buffet Process Models matr
Page 86 and 87: 4 Indian Buffet Process Models In t
Page 88 and 89: 4 Indian Buffet Process Models α z
Page 90 and 91: 4 Indian Buffet Process Models α
Page 92 and 93: 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
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4 Indian Buffet Process Models Figu
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4 Indian Buffet Process Models pres
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4 Indian Buffet Process Models ε
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4 Indian Buffet Process Models LL P
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4 Indian Buffet Process Models P+ P
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4 Indian Buffet Process Models tEBA
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4 Indian Buffet Process Models dist
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5 Conclusions has been defined as a
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A Details of Derivations for the St
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B Mathematical Appendix B.1 Dirichl
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p3 α 1 0.5 0 0 0.5 0.4 0.3 0.2 0.1
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Construction of A Process B.4 Equal
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Bibliography D. Aldous. Exchangeabi
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Bibliography T. S. Ferguson. Prior
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Bibliography L. F. James and J. W.
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Bibliography R. M. Neal. Probabilis
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Bibliography Y. W. Teh, M. I. Jorda
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