Index: Teh 2010 - Dirichlet Process

Teh 2010 - Dirichlet Process

Routing Summary

Fully captures Teh (2010), Dirichlet Process, Encyclopedia of Machine Learning (13 pp.). Six notes cover the definition, posterior, urn/CRP, stick-breaking, DP mixtures and the reference map.

• Need the paper on one page, source map or the PyMC examples that use it? → Teh 2010 - Dirichlet Process - Overview
• Need the definition, moments or posterior conjugacy? → Teh 2010 - DP Definition and Posterior Conjugacy
• Need the urn predictive, CRP, or the prior on the number of clusters? → Teh 2010 - Blackwell-MacQueen Urn and Chinese Restaurant Process
• Need stick-breaking, truncation levels or a PyMC sketch? → Teh 2010 - Stick-Breaking Construction
• Need DP mixtures, density estimation, or the practical checklist? → Teh 2010 - DP Mixture Models and Applications
• Need extensions (PY, HDP, dependent DP) or the reference map? → Teh 2010 - Extensions and Reference Map

Concept Map

Concept	Note	Type	Depends On	Key Result
Dirichlet process	Teh 2010 - DP Definition and Posterior Conjugacy	definition	Dirichlet distribution	Dir marginals on every partition
Posterior conjugacy	Teh 2010 - DP Definition and Posterior Conjugacy	theorem	DP definition	$\text{DP}(\alpha +n,\cdot )$
Blackwell-MacQueen urn	Teh 2010 - Blackwell-MacQueen Urn and Chinese Restaurant Process	theorem	posterior	predictive $\propto \alpha H+\sum \delta$
CRP; number of clusters	Teh 2010 - Blackwell-MacQueen Urn and Chinese Restaurant Process	theorem	urn	$E[m]=\alpha (\psi (\alpha +n)-\psi (\alpha ))$
Stick-breaking	Teh 2010 - Stick-Breaking Construction	theorem	DP definition	${\pi }_k={\beta }_k\prod (1-{\beta }_l)$
DP mixture	Teh 2010 - DP Mixture Models and Applications	definition	stick-breaking, CRP	infinite mixture, $K\sim \alpha \log n$
Extensions, reference map	Teh 2010 - Extensions and Reference Map	concept	all	PY, HDP, dependent DP

Notes

• Teh 2010 - Dirichlet Process - Overview — CONTAINS: research question, key results, Source Map, motivating PyMC examples E26/E30/E75.
• Teh 2010 - DP Definition and Posterior Conjugacy — CONTAINS: Def. DP, moments theorem, posterior theorem with proof sketch, variance example.
• Teh 2010 - Blackwell-MacQueen Urn and Chinese Restaurant Process — CONTAINS: urn theorem, CRP, number-of-clusters theorem, simulation code.
• Teh 2010 - Stick-Breaking Construction — CONTAINS: Sethuraman theorem, truncation levels, PyMC sketch.
• Teh 2010 - DP Mixture Models and Applications — CONTAINS: finite-limit and DP mixture definitions, applications, practical checklist.
• Teh 2010 - Extensions and Reference Map — CONTAINS: generalisations, future directions, 18-item reference map.

Sources

• Teh 2010 - Dirichlet Process — Teh YW (2010), Dirichlet Process, in Encyclopedia of Machine Learning (author PDF, 13 pp.).

See Also

Griffiths 2011 - The Indian Buffet Process - Overview, De Blasi 2015 - Gibbs-Type Priors - Overview, Nonparametric Models Overview, Monsters and Mixtures