Nonparametric Bayesian Discrete Latent Variable Models for ...

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List of Algorithms Symbol Meaning general ∝ proportional to; e.g. p(x) ∝ f(x) means p(x) is equal to f(x) times a factor that is independent of x ∼ distributed according to; e.g. x ∼ F (x | θ) means x has distribution F (θ) ⊗ elementwise multiplication δθ(·) probability measure concentrated at θ A\B set difference D dimension of input space DKL(pq) the KL divergence between the density p and q E f(φ) expectation of function f taken with respect to the distribution of φ HN Nth harmonic number, HN = N i=1 1/i I(A) the indicator function for a measurable set A; I(A) = 1 if A is true, 0 otherwise L( ˆ φ, φ) loss encountered by predicting ˆ φ when the true value is φ L(X | Θ) likelihood of the parameter(s) Θ for the data points X N number of training points xi ith data point X data matrix containing the set of observations {x1, . . . , xN} DP D(α1, . . . , αk) k-dimensional Dirichlet distribution DP (α, G0) Dirichlet process with concentration parameter α and base distribution G0 ci indicator variable for xi showing the component assignment c set of all indicator variables {c1, . . . , cN} {θi} n 1 sequence of random variables θi, i = 1, . . . , n θi parameter associated with xi θ−i set of all parameters other than i φk parameter associated with kth component (feature) πk mixing proportion for the kth mixture component nk the number of data points assigned to component k n.
Symbol Meaning IBP Z binary latent feature matrix List of Algorithms zik an entry of matrix Z zi ith row of Z, features of ith customer zk kth column of Z, kth feature vector [Z] equivalence class of binary matrix Z mk the number of customers that has the kth dish m.
Page 1: Nonparametric Bayesian Discrete Lat
Page 4 and 5: Matrizen mit unendlich vielen Spalt
Page 7 and 8: Contents Zusammenfassung iii Abstra
Page 9: List of Algorithms 1 Gibbs sampling
Page 13: Notation Matrices are capitalized a
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
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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
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4 Indian Buffet Process Models colu
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4 Indian Buffet Process Models Pois
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4 Indian Buffet Process Models z α
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4 Indian Buffet Process Models For
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4 Indian Buffet Process Models ciat
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4 Indian Buffet Process Models rati
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4 Indian Buffet Process Models repr
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4 Indian Buffet Process Models samp
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4 Indian Buffet Process Models feat
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4 Indian Buffet Process Models Algo
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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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Nonparametric Bayesian Discrete Latent Variable Models for ...

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