Index: Griffiths 2011 - The Indian Buffet Process

Griffiths 2011 - The Indian Buffet Process

Routing Summary

Fully captures Griffiths and Ghahramani (2011), The Indian Buffet Process: An Introduction and Review, JMLR 12:1185-1224 (40 pp.). Eight notes cover the CRP review, latent feature models, the infinite limit, the IBP and its properties, Gibbs sampling with the linear-Gaussian model, applications, and extensions.

• Need the paper on one page, headline results or the Source Map? → Griffiths 2011 - The Indian Buffet Process - Overview
• Need the CRP derivation by limits (the template)? → Griffiths 2011 - Infinite Mixtures and the CRP Review
• Need the beta-Bernoulli finite model and sparsity bound? → Griffiths 2011 - Latent Feature Models and the Finite Beta-Bernoulli Prior
• Need left-ordered form and the limit theorem? → Griffiths 2011 - Equivalence Classes and the Infinite Limit
• Need the buffet process, $P(Z)$, $K_{+}\sim \text{Poisson}(\alpha H_N)$? → Griffiths 2011 - The Indian Buffet Process and Its Properties
• Need Gibbs conditionals and the linear-Gaussian marginal likelihood? → Griffiths 2011 - Gibbs Sampling and the Linear-Gaussian Model
• Need the application list? → Griffiths 2011 - Applications of the IBP
• Need the two-parameter IBP, stick-breaking, beta process, Markov IBP? → Griffiths 2011 - Two-Parameter IBP, Stick-Breaking and Beta Process

Concept Map

Concept	Note	Type	Depends On	Key Result
Finite beta-Bernoulli prior	Griffiths 2011 - Latent Feature Models and the Finite Beta-Bernoulli Prior	definition	CRP review	$E[\text{ones}]\le N\alpha$
lof equivalence	Griffiths 2011 - Equivalence Classes and the Infinite Limit	definition	finite prior	column-permutation classes
Infinite limit	Griffiths 2011 - Equivalence Classes and the Infinite Limit	theorem	lof classes	Eq. 14
IBP	Griffiths 2011 - The Indian Buffet Process and Its Properties	definition	limit	Poisson($\alpha /i$) new dishes
Properties	Griffiths 2011 - The Indian Buffet Process and Its Properties	theorem	IBP	$K_{+}\sim \text{Poisson}(\alpha H_N)$
Linear-Gaussian marginal	Griffiths 2011 - Gibbs Sampling and the Linear-Gaussian Model	theorem	IBP	depends on $K_{+}$ columns only
Two-parameter IBP	Griffiths 2011 - Two-Parameter IBP, Stick-Breaking and Beta Process	definition	IBP	decouples sparsity and $K_{+}$
IBP stick-breaking	Griffiths 2011 - Two-Parameter IBP, Stick-Breaking and Beta Process	theorem	DP stick-breaking	cumulative products of Beta$(\alpha ,1)$

Notes

• Griffiths 2011 - The Indian Buffet Process - Overview — CONTAINS: question, contributions, Source Map, motivating example E31, marketing relevance.
• Griffiths 2011 - Infinite Mixtures and the CRP Review — CONTAINS: finite class prior, CRP limit theorem, Gibbs, three-customer example.
• Griffiths 2011 - Latent Feature Models and the Finite Beta-Bernoulli Prior — CONTAINS: $Z\odot V$ decomposition, beta-Bernoulli definition, marginal, sparsity bound.
• Griffiths 2011 - Equivalence Classes and the Infinite Limit — CONTAINS: histories, lof, limit theorem and proof sketch, left-ordering example.
• Griffiths 2011 - The Indian Buffet Process and Its Properties — CONTAINS: IBP definition, $P(Z)$, exchangeable IBP, Poisson view, properties, simulation code.
• Griffiths 2011 - Gibbs Sampling and the Linear-Gaussian Model — CONTAINS: Gibbs conditionals, marginal likelihood theorem, demonstrations, verification code, PyMC sketch.
• Griffiths 2011 - Applications of the IBP — CONTAINS: Sec. 6.1-6.9 table, conclusions.
• Griffiths 2011 - Two-Parameter IBP, Stick-Breaking and Beta Process — CONTAINS: two-parameter IBP, stick-breaking, beta process, Markov and phylogenetic IBP.

Sources

• Griffiths Ghahramani 2011 - The Indian Buffet Process An Introduction and Review — Griffiths TL, Ghahramani Z (2011), JMLR 12:1185-1224.

See Also

Teh 2010 - Dirichlet Process - Overview, De Blasi 2015 - Gibbs-Type Priors - Overview, Nonparametric Models Overview, Factor Analysis and PPCA