Markov Chain Sampling Methods for Dirichlet Process Mixture Models

Neal, Radford M.

doi:10.1080/10618600.2000.10474879

Cited by 1,493 publications

(1,362 citation statements)

References 15 publications

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“…Common control design for cooperative spectrum prediction in a multi-primary, user's environment is yet to develop in the spectrum prediction literature. Analysis of cooperative prediction using hierarchical Dirichlet processes is an interesting proposal to model cooperative spectrum prediction, that is not explored in SOP literature [40].…”

Section: Cooperation and Contentionmentioning

confidence: 99%

“…Moreover, mixture models are more complex but allow empirical measurements-based source estimation. An example would be Dirichlet mixture process which often used to generate mixture prior distributions, but tracing convergence bounds becomes increasingly difficult for nonGaussian mixtures for example [20,28,40]. Convergence bounds are calculated only for limited Bayesian mixture class/prior distribution pairs (for example, uniform prior/Epanchinkov kernel) [107].…”

Section: Validity and Complexitymentioning

confidence: 99%

“…A common non-parametric Bayesian method is the Dirichlet process D(α, G), where α is concentration parameter, and G is the distribution over θ ∈ M. Samples of θ t at each time instant t are calculated iteratively from G using Monte-Carlo Markov chain methods. Infinite mixture model allows dynamic classification of data into clusters without having to specify the number of clusters in advance [40][41][42].…”

Section: Infinite Mixture Modelsmentioning

confidence: 99%

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Statistical spectrum occupancy prediction for dynamic spectrum access: a classification

Eltom

Kandeepan

Evans

et al. 2018

J Wireless Com Network

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Spectrum scarcity due to inefficient utilisation has ignited a plethora of dynamic spectrum access solutions to accommodate the expanding demand for future wireless networks. Dynamic spectrum access systems allow secondary users to utilise spectrum bands owned by primary users if the resulting interference is kept below a pre-designated threshold. Primary and secondary user spectrum occupancy patterns determine if minimum interference and seamless communications can be guaranteed. Thus, spectrum occupancy prediction is a key component of an optimised dynamic spectrum access system. Spectrum occupancy prediction recently received significant attention in the wireless communications literature. Nevertheless, a single consolidated literature source on statistical spectrum occupancy prediction is not yet available in the open literature. Our main contribution in this paper is to provide a statistical prediction classification framework to categorise and assess current spectrum occupancy models. An overview of statistical sequential prediction is presented first. This statistical background is used to analyse current techniques for spectrum occupancy prediction. This review also extends spectrum occupancy prediction to include cooperative prediction. Finally, theoretical and implementation challenges are discussed.

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Section: Cooperation and Contentionmentioning

confidence: 99%

Section: Validity and Complexitymentioning

confidence: 99%

Section: Infinite Mixture Modelsmentioning

confidence: 99%

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Statistical spectrum occupancy prediction for dynamic spectrum access: a classification

Eltom

Kandeepan

Evans

et al. 2018

J Wireless Com Network

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“…The goal state is an assignment that results in an acceptable clustering based on a clustering criterion such as m.s.e. A variety of inference methods based on Gibbs sampling (which is an MC sampling algorithm) have been proposed for inference in DPMM [23]. The collapsed Gibbs sampling algorithm (algorithm 3 in [23]) is suitable for our use of DPMM for clustering as we are only interested in knowing the cluster assignments (z i 's) and not the actual cluster parameters (θ k 's).…”

Section: (D) Clusteringmentioning

confidence: 99%

“…A variety of inference methods based on Gibbs sampling (which is an MC sampling algorithm) have been proposed for inference in DPMM [23]. The collapsed Gibbs sampling algorithm (algorithm 3 in [23]) is suitable for our use of DPMM for clustering as we are only interested in knowing the cluster assignments (z i 's) and not the actual cluster parameters (θ k 's). It is an iterative algorithm that in each iteration updates the values of z i for each data point one at a time.…”

Section: (D) Clusteringmentioning

confidence: 99%

Markov chain algorithms: a template for building future robust low-power systems

Deka

Birklykke

Duwe

et al. 2014

Phil. Trans. R. Soc. A.

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Although computational systems are looking towards post CMOS devices in the pursuit of lower power, the expected inherent unreliability of such devices makes it difficult to design robust systems without additional power overheads for guaranteeing robustness. As such, algorithmic structures with inherent ability to tolerate computational errors are of significant interest. We propose to cast applications as stochastic algorithms based on Markov chains (MCs) as such algorithms are both sufficiently general and tolerant to transition errors. We show with four example applications—Boolean satisfiability, sorting, low-density parity-check decoding and clustering—how applications can be cast as MC algorithms. Using algorithmic fault injection techniques, we demonstrate the robustness of these implementations to transition errors with high error rates. Based on these results, we make a case for using MCs as an algorithmic template for future robust low-power systems.

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Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Liu

Elshall

et al. 2016

Water Resources Research

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Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamic integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. The thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.

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Markov Chain Sampling Methods for Dirichlet Process Mixture Models

Cited by 1,493 publications

References 15 publications

Statistical spectrum occupancy prediction for dynamic spectrum access: a classification

Statistical spectrum occupancy prediction for dynamic spectrum access: a classification

Markov chain algorithms: a template for building future robust low-power systems

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

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