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Consistency Analysis for the Doubly Stochastic Dirichlet Process [article]

Xing Sun, Nelson H.C. Yung, Edmund Y. Lam, Hayden K.-H. So
2016 arXiv   pre-print
This technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability.  ...  This report is also a support document for the paper "Computationally Efficient Hyperspectral Data Learning Based on the Doubly Stochastic Dirichlet Process".  ...  CONCLUSION Contributions can be regarded in two parts for this technical report: 1) we proved the consistency for the number of components in Doubly Stochastic Dirichlet process with exponential convergence  ... 
arXiv:1605.07358v1 fatcat:n4xvvsy77zcjzhzedlkisiyplq

The Gaussian Free Field and SLE4 on Doubly Connected Domains

Christian Hagendorf, Denis Bernard, Michel Bauer
2010 Journal of statistical physics  
Extensions of Schramm's formula to doubly connected domains are given for the standard Dirichlet and Neumann conditions and a relation to first-exit problems for Brownian bridges is established.  ...  It is shown how this relation allows to define chordal SLE(4) processes on doubly connected domains, describing traces that are anchored on one of the two boundary components.  ...  This simplification, together with our analysis of the null vector equations and martingales on doubly connected domains for κ = 4, suggests that a similar reduction to an elementary stochastic process  ... 
doi:10.1007/s10955-010-9980-1 fatcat:sc6wnssm2ffxfhraz6e3jqdj4y

Abstracts of Papers

1955 The Annals of Mathematical Statistics  
This material includes the N-dimensional spherical, general spherical, and general Dirichlet domain processes.  ...  to the Dirichlet problem.  ... 
doi:10.1214/aoms/1177728502 fatcat:3vdii7no5rafrbl2z72hwda6qu

Page 1972 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
Summary: “An algorithm for simulating the class of neutral to the right processes is described. The mixture of Dirichlet processes (MDP) model has proved to be successful in a variety of con- texts.  ...  ); Damien, Paul (1-MI-SMS; Ann Arbor, MI) Sampling methods for Bayesian nonparametric inference involving stochastic processes.  ... 

The Pólya sum kernel and Bayes estimation [article]

Mathias Rafler
2012 arXiv   pre-print
Moreover, we extend this result to doubly stochastic Poisson-Gamma priors and give conditions under which one can identify the Bayes estimator for the intensity.  ...  the construction of the so-called Papangelou processes.  ...  [1] for mixed Dirichlet processes.  ... 
arXiv:1202.4696v2 fatcat:ujspakzibvhsfkow4i5aqmtkkm

Bayesian Inference for Non-Markovian Point Processes [chapter]

Peter Guttorp, Thordis L. Thorarinsdottir
2011 Lecture Notes in Statistics  
We focus on non-Markovian processes, specifically Poisson and related models, doubly stochastic models, and cluster models.  ...  In this paper, we review the Bayesian contributions to inference for point processes.  ...  Doubly stochastic processes The doubly stochastic Poisson process, introduced by Cox (1955) and so named by Bartlett (1963) is obtained by letting the rate λ(t) of the Poisson process vary according  ... 
doi:10.1007/978-3-642-17086-7_4 fatcat:l6dudx26krfjnawrndvjcqlypy

Bayesian Nonparametrics in Topic Modeling: A Brief Tutorial [article]

Alexander Spangher
2015 arXiv   pre-print
Although the field shows a lot of promise, inference in many models, including Hierachical Dirichlet Processes (HDP), remain prohibitively slow.  ...  I will show a comparison between different non-parametric models and the current state-of-the-art parametric model, Latent Dirichlet Allocation (LDA).  ...  Aravkin for a truly excellent semester, and my coworkers at the New York Times-especially Daeil Kim-for suggestions and moral support.  ... 
arXiv:1501.03861v1 fatcat:jbgoycyaynbfno3rqoumpvrlo4

The Doubly Correlated Nonparametric Topic Model

Dae Il Kim, Erik B. Sudderth
2011 Neural Information Processing Systems  
We propose a doubly correlated nonparametric topic (DCNT) model, the first model to simultaneously capture all three of these properties.  ...  Desirable traits include the ability to incorporate annotations or metadata associated with documents; the discovery of correlated patterns of topic usage; and the avoidance of parametric assumptions,  ...  , AFRL, or the U.S.  ... 
dblp:conf/nips/KimS11 fatcat:g6tnp6wmvnh7jilzkcysd5i2ou

Random bistochastic matrices

Valerio Cappellini, Hans-Jürgen Sommers, Wojciech Bruzda, Karol Życzkowski
2009 Journal of Physics A: Mathematical and Theoretical  
For matrices of order N = 2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution.  ...  The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.  ...  Acknowledgments The authors gratefully acknowledge financial support provided by the EU Marie Curie Host Fellowships for Transfer of Knowledge Project COCOS (contract no MTKD-CT-2004-517186) and the SFB  ... 
doi:10.1088/1751-8113/42/36/365209 fatcat:wrjlot2nibh37mhjjitbxxwu2a

Page 6228 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews  
Mertsbakh [Ely Merzbach], Set-indexed stochastic processes and predictability (57-63); O.  ...  After asserting the need foranalysis on fractals” in Section 1, the author gives examples of it in Sections 2-5 by demonstrating a well-formulated analytical the- ory using the Laplace operator, the  ... 

Book Review: The $P\left( \Phi \right)_2$ euclidean (quantum) field theory

John L. Challifour
1975 Bulletin of the American Mathematical Society  
stochastic processes.  ...  This would have settled questions concerning the internal consistency of this framework as well as suggesting avenues for further development.  ... 
doi:10.1090/s0002-9904-1975-13869-9 fatcat:h7523s7qkzbpvgs5vuiyucraqe

Online Sparse Collapsed Hybrid Variational-Gibbs Algorithm for Hierarchical Dirichlet Process Topic Models [chapter]

Sophie Burkhardt, Stefan Kramer
2017 Lecture Notes in Computer Science  
We propose a new sampling method that enables the application of the idea to the nonparametric version of LDA, hierarchical Dirichlet process topic models.  ...  Topic models for text analysis are most commonly trained using either Gibbs sampling or variational Bayes.  ...  Hierarchical Dirichlet Processes For hierarchical Dirichlet process (HDP) topic models [16] , the multinomial distribution θ from LDA is drawn from an HDP instead of a Dirichlet distribution: θ ∼ DP (  ... 
doi:10.1007/978-3-319-71246-8_12 fatcat:wfgwekso5naudk3rcbsnokn26q

Random Bistochastic Matrices [article]

V. Cappellini, H.-J. Sommers, W. Bruzda, K. Zyczkowski
2009 arXiv   pre-print
For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution.  ...  The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.  ...  Acknowledgements The authors gratefully acknowledges financial support provided by the EU Marie Curie Host Fellowships for Transfer of Knowledge Project COCOS (contract number MTKD-CT-2004-517186) and  ... 
arXiv:0711.3345v2 fatcat:6surdyvwfjbexdpxmamq3ygaai

Entropy production of doubly stochastic quantum channels

Alexander Müller-Hermes, Daniel Stilck França, Michael M. Wolf
2016 Journal of Mathematical Physics  
We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state.  ...  In the last part of this work we study entropy production estimates of discrete-time doubly-stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the  ...  These inequalities turn out to be useful for the analysis of quantum memories (see section 5.1).  ... 
doi:10.1063/1.4941136 fatcat:ubdzwsa565hodmkagurecyy55y

Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes

Junyu Xuan, Jie Lu, Guangquan Zhang, Richard Yi Da Xu, Xiangfeng Luo
2018 IEEE Transactions on Neural Networks and Learning Systems  
In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian Buffet Processes (dIBP).  ...  Our work is seen to be more flexible than Gaussian Process (GP)-based and Hierarchial Beta Process (HBP)-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations  ...  ACKNOWLEDGMENT Research work reported in this paper was partly supported by the Australian Research Council (ARC) under discovery grant DP140101366.  ... 
doi:10.1109/tnnls.2017.2676817 pmid:28422690 fatcat:etndib7dgzdidg4jzyiwxawcmu
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