Combinatorial Stochastic Processes
Jim Pitman
- Vol. 1875
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In this paper, the Brownian forest and the additive coalescent were constructed for random walks and random forests, respectively, and the Bessel process was used for random mappings.Abstract:
Preliminaries.- Bell polynomials, composite structures and Gibbs partitions.- Exchangeable random partitions.- Sequential constructions of random partitions.- Poisson constructions of random partitions.- Coagulation and fragmentation processes.- Random walks and random forests.- The Brownian forest.- Brownian local times, branching and Bessel processes.- Brownian bridge asymptotics for random mappings.- Random forests and the additive coalescent.read more
Citations
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Hierarchical Dirichlet Processes
TL;DR: This work considers problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups, and considers a hierarchical model, specifically one in which the base measure for the childDirichlet processes is itself distributed according to a Dirichlet process.
Proceedings Article
Infinite latent feature models and the Indian buffet process
TL;DR: A probability distribution over equivalence classes of binary matrices with a finite number of rows and an unbounded number of columns is defined, suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features.
Proceedings Article
Learning systems of concepts with an infinite relational model
TL;DR: A nonparametric Bayesian model is presented that discovers systems of related concepts and applies the approach to four problems: clustering objects and features, learning ontologies, discovering kinship systems, and discovering structure in political data.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.