Exact and approximate sum representations for the Dirichlet process

By Hemant Ishwaran, Mahmoud Zarepour. 2002

348 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/315a9d88925d703104109aac6db82bc31a0fa6b8

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Citations in the corpus

Hierarchical Dirichlet Processes (2006, methodology): “More sophisticated methods—such as split-and-merge methods (Jain and Neal 2000) and variational methods (Blei and Jordan 2005)—have shown promise for DPs, and we expect that they will prove useful for hierarchical DPs as well.”
Object Recognition by Scene Alignment (2007, background): “fiths, Engen, and McCloskey [8, 11, 16] with concentration parameter α.”
Discovering linguistic structures in speech: models and applications (2014, methodology): “The inference scheme of setting an upper bound K on the number of clusters that a Dirichlet process finds is referred to as the degreeK weak limit approximation to the Dirichlet process [72], which has been exploited in the inference algorithms of other nonparametric models and shown to work well [4”
Multi-task compressive sensing with Dirichlet process priors (2008, methodology): “This model is a finite approximation to the DP-based model, in the sense that as J → ∞ this prior corresponds to DP with λ = 1 [30][22].”
A Sticky HDP-HMM With Application to Speaker Diarization (2009, methodology): “Another method is to consider thed greeL weak limit approximationto the DP (Ishwaran and Zarepour, 2002b), GEML(α) , Dir(α/L, . . . , α/L),(5.4) whereL is a number that exceeds the total number of expected HMM states.”
Introduction to the Dirichlet Distribution and Related Processes (2010, background): “If we call the resulting probability measure PN , then PN (g) → P (g) almost surely as N →∞ for any bounded continuous function g : X → R, where PN (g) = ∫ gdPNand P (g) = ∫ gdP [7].”
DIRICHLET PRIOR SIEVES IN FINITE NORMAL MIXTURES (2002, background): “For 2(a) see Ishwaran and Zarepour (2002) , while 2(b) can be proven from the results in Kingman (1975, Section 6) or Kingman (1993, Section 9.3) pertaining to the Poisson-Dirichlet distribution.”
Generalized spatial dirichlet process models (2007, methodology): “Ishwaran & Zarepour, 2002b for a review of stick-breaking univariate priors.”
Probabilistic grammars and hierarchical Dirichlet processes (2018, background): “, 1 K ) prior (e), which approximates a DP prior (Ishwaran and Zarepour, 2002), does provide this sparsity if we use mean-field.”
Generalized weighted Chinese restaurant processes for species sampling mixture models (2003, methodology): “Limits under different choices of κ were studied by Ishwaran and Zarepour (2002b).”
A Tutorial on Bayesian Nonparametric Models (2011, methodology): “WhenK →∞, this mixture converges to a Dirichlet process mixture model (Neal, 1992; Rasmussen, 2000; Ishwaran and Zarepour, 2002).”
Mixture Modeling for Marked Poisson Processes (2010, positive): “As discussed in Ishwaran and Zarepour (2002), using results from Pitman (1996), a draw for G | θ?, s, α, ψ can be represented as q0G∗(·) + ∑m j=1 qjδθ?j (·), where G ∗ | α, ψ ∼ DP(α,G0(ψ)), and, independently of G∗, (q0, q1, ..., qm) | α, s ∼ Dir(q0, q1, ..., qm;α, n1, ..., nm).”