Combinatorial Stochastic Processes

By Jim Pitman. 2006

1,356 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b341012b256a2ce2cb61bf9203717daacc3e99ca

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Citations in the corpus

Scaling limits of random planar maps with a unique large face (2012, methodology): “ariables distributed as N. (This is shown in [36] as a consequence of a corresponding result for random walks by Armenda´riz and Loulakis [5].) Furthermore, it is well known (see, e.g., [34, 35, 48], [49], Section 6.1, [29], Theorem 15.5) that if ξi, i=1,2,..., is a sequence of independent random va”
A Hierarchical Bayesian Language Model Based On Pitman-Yor Processes (2006, methodology): “, 1995) where each hidden variable is distributed according to a Pitman-Yor process, a nonparametric generalization of the Dirichlet distribution that is widely studied in the statistics and probability theory communities (Pitman and Yor, 1997; Ishwaran and James, 2001; Pitman, 2002).”
Deep Generative Models with Stick-Breaking Priors (2016, background): “erguson, 1973). In this case, the name for the joint distribution over the inﬁnite sequence of stick-breaking weights is the Grifﬁths, Engen and McCloskey distribution with concentration parameter 0 (Pitman, 2002): (ˇ 1;ˇ 2;:::) ˘GEM( 0). 2 Published as a conference paper at ICLR 2017 3 SGVB FOR GEM”
Spinal partitions and invariance under re-rooting of continuum random trees (2007, background): “13 of [32] ensure that nα−1Kn converges a.”
Dirichlet Variational Autoencoder (2019, background): “Additionally, the Griffiths-Engen-McCloskey (GEM) distribution (Pitman, 2002), which is the prior distribution of the SBVAE, is difficult to model the multi-modality because the sampling procedure of the GEM distribution is affected by the rich-get-richer phenomenon, so a few components tend to domi”
Stochastic variational inference (2012, background): “For example, it is a normalized gamma process (Ferguson, 1973), and its marginalization gives the Chinese restaurant process (Pitman, 2002).”
Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process (2003, background): “has a Poisson distribution with parameter µ(k) = sk/k. Proof. Let {Lb(k)} k≥1 be independent Poisson variables with parameters {µ(k)}, and deﬁne Nb= P k≥1 k Lb(k). Then formula (99) of Section 1.4 in Pitman (2002) in conjunction with Example 5 there, imply that for each n>0, the conditional distr”
Distance dependent Chinese restaurant processes (2009, neutral): “The Chinese restaurant process (CRP) is a probability distribution over partitions (Pitman, 2002).”
The Ubiquitous Ewens Sampling Formula (2016, background): “When α > 0, Pitman [76] obtains the following limit law.”
Probability and Mathematical Genetics: More uses of exchangeability: representations of complex random structures (2009, background): “plain with hindsight how Kingman’sworkon exchangeable randompartitions ﬁtsthistheme. 3.1 Exchangeable random partitions and Kingman’s paintbox theorem The material here is covered in detail in Pitman [51] Chapters 2-4. Given a discrete sub-probability distribution, one can write the probabilities in”
Random trees and applications (2005, background): “See Chapters 5 and 6 of Pitman [36], and the references therein, for more results about the connections between trees, random walks and Brownian motion.”
The Infinite PCFG Using Hierarchical Dirichlet Processes (2007, methodology): “The Dirichlet hyperparameter α controls how uniform this distribution is: as α increases, it becomes increasingly likely that the components have equal probability.”
The Brownian limit of separable permutations (2016, background): “n Random mappings and Brownian bridges; Random trees and Brownian trees; Random graphs and Brownian motion. THE BROWNIAN LIMIT OF SEPARABLE PERMUTATIONS 7 A very good reference for these topics is [37]. Theorem 1.6 ﬁts naturally in this body of literature. Note that the fact that separable permutati”