Computations of Mixtures of Dirichlet Processes

1986 ◽  
Vol 7 (1) ◽  
pp. 60-71 ◽  
Author(s):  
Lynn Kuo
Keyword(s):  
Dirichlet Processes

Hierarchical Dirichlet Processes and Their Applications: A Survey

2011 ◽  
Vol 37 (4) ◽  
pp. 389-407 ◽  
Author(s):  
Jian-Ying ZHOU ◽  
Fei-Yue WANG ◽  
Da-Jun ZENG
Keyword(s):  
Dirichlet Processes ◽  
Hierarchical Dirichlet Processes

scholarly journals Zipf’s, Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 752 ◽  
Author(s):  
Francesca Tria ◽  
Vittorio Loreto ◽  
Vito Servedio
Keyword(s):  
Ad Hoc ◽  
Ecological Systems ◽  
Dirichlet Processes ◽  
Urn Model ◽  
Modeling Framework ◽  
Self Consistent ◽  
Pólya’S Urn ◽  
Innovation Rate ◽  
Innovation Processes ◽  
Simple Modeling

Zipf’s, Heaps’ and Taylor’s laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the scaling of fluctuations for systems as diverse as written texts and cities, ecological systems and stock markets. Many modeling schemes have been proposed in literature to explain those laws, but only recently a modeling framework has been introduced that accounts for the emergence of those laws without deducing the emergence of one of the laws from the others or without ad hoc assumptions. This modeling framework is based on the concept of adjacent possible space and its key feature of being dynamically restructured while its boundaries get explored, i.e., conditional to the occurrence of novel events. Here, we illustrate this approach and show how this simple modeling framework, instantiated through a modified Pólya’s urn model, is able to reproduce Zipf’s, Heaps’ and Taylor’s laws within a unique self-consistent scheme. In addition, the same modeling scheme embraces other less common evolutionary laws (Hoppe’s model and Dirichlet processes) as particular cases.

scholarly journals Kernel Analysis Based on Dirichlet Processes Mixture Models

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 857
Author(s):  
Jinkai Tian ◽  
Peifeng Yan ◽  
Da Huang
Keyword(s):  
Mixture Models ◽  
Crucial Role ◽  
Gaussian Mixture Models ◽  
Gaussian Process Regression ◽  
Gaussian Mixture ◽  
Spectral Domain ◽  
Dirichlet Processes ◽  
Number Of Components ◽  
Kernel Analysis ◽  
Nonparametric Bayesian Models

Kernels play a crucial role in Gaussian process regression. Analyzing kernels from their spectral domain has attracted extensive attention in recent years. Gaussian mixture models (GMM) are used to model the spectrum of kernels. However, the number of components in a GMM is fixed. Thus, this model suffers from overfitting or underfitting. In this paper, we try to combine the spectral domain of kernels with nonparametric Bayesian models. Dirichlet processes mixture models are used to resolve this problem by changing the number of components according to the data size. Multiple experiments have been conducted on this model and it shows competitive performance.

Lower order perturbations of Dirichlet processes

2003 ◽  
Vol 15 (2) ◽  
Author(s):  
M. Röckner ◽  
T. S. Zhang
Keyword(s):  
Lower Order ◽  
Dirichlet Processes

scholarly journals On the Convergence of Dirichlet Processes

Bernoulli ◽  
1999 ◽  
Vol 5 (4) ◽  
pp. 615 ◽  
Author(s):  
François Coquet ◽  
Leszek Słomiński ◽  
Francois Coquet ◽  
Leszek Slominski
Keyword(s):  
Dirichlet Processes
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