A partially collapsed Gibbs sampler with accelerated convergence for EEG source localization

Costa, Facundo; Batatia, Hadj; Oberlin, Thomas; Tourneret, Jean-Yves

doi:10.1109/ssp.2016.7551743

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…Although this strategy can significantly decrease the complexity of the sampling process, it must be implemented with care to guarantee that the desired stationary distribution is preserved. Applications of PCGS algorithms can be found in [66][67][68].…”

Section: Alternative Ii: Eliminate the Coupling Induced By H D(σ (T) )Hmentioning

confidence: 99%

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

Marnissi

Chouzenoux

Benazza-Benyahia

et al. 2018

Entropy

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Abstract:In this paper, we are interested in Bayesian inverse problems where either the data fidelity term or the prior distribution is Gaussian or driven from a hierarchical Gaussian model. Generally, Markov chain Monte Carlo (MCMC) algorithms allow us to generate sets of samples that are employed to infer some relevant parameters of the underlying distributions. However, when the parameter space is high-dimensional, the performance of stochastic sampling algorithms is very sensitive to existing dependencies between parameters. In particular, this problem arises when one aims to sample from a high-dimensional Gaussian distribution whose covariance matrix does not present a simple structure. Another challenge is the design of Metropolis-Hastings proposals that make use of information about the local geometry of the target density in order to speed up the convergence and improve mixing properties in the parameter space, while not being too computationally expensive. These two contexts are mainly related to the presence of two heterogeneous sources of dependencies stemming either from the prior or the likelihood in the sense that the related covariance matrices cannot be diagonalized in the same basis. In this work, we address these two issues. Our contribution consists of adding auxiliary variables to the model in order to dissociate the two sources of dependencies. In the new augmented space, only one source of correlation remains directly related to the target parameters, the other sources of correlations being captured by the auxiliary variables. Experiments are conducted on two practical image restoration problems-namely the recovery of multichannel blurred images embedded in Gaussian noise and the recovery of signal corrupted by a mixed Gaussian noise. Experimental results indicate that adding the proposed auxiliary variables makes the sampling problem simpler since the new conditional distribution no longer contains highly heterogeneous correlations. Thus, the computational cost of each iteration of the Gibbs sampler is significantly reduced while ensuring good mixing properties.

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Section: Alternative Ii: Eliminate the Coupling Induced By H D(σ (T) )Hmentioning

confidence: 99%

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

Marnissi

Chouzenoux

Benazza-Benyahia

et al. 2018

Entropy

View full text Add to dashboard Cite

show abstract

“…Note, to ensure the Markov chains faithfully coming from

\propto I false{H [T^{- 1} ({boldZ}_{normalU}), Z, u, γ] \leq 0 false} P false(Z false) ϕ false(Z_{U} false)

, it is required that the selected marginalised‐out variable(s) must always be sampled after those variables following the reduced marginal distribution, meanwhile, before variables, if any, conditioned on it. Although the mechanism proves to be able to accelerate the Markov chain mixing, performance decay is still observed in the case of high‐dimensional application, for instance, convincing evidence can be found in [35]. In a nutshell, the variety of limited number of high‐dimensional training vector samples is bound to lock locally, or equivalently, the obtained Markov chains look like being not irreducible in the limited sample pool.…”

Section: Methodologiesmentioning

confidence: 99%

Tracing spinning reserve inadequacy risk via hybrid importance sampling with an optimised partially collapsed Gibbs sampler

Wang

2021

IET Renewable Power Gen

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From the simulation perspective, spinning reserve risk evaluation of power system is commonly a rare-event assessing issue, for which importance sampling is an appealing solution technique. This paper proposes a hybrid importance sampling method for tracing spinning reserve inadequacy risk of power system integrating with renewables. The proposed method is oriented towards a generic high-dimensional integral calculus, which allows for continuous and discrete random variables mixed together for casting kinds of risk indices. To improve the robustness in high-dimensional applications, a partially collapsed Gibbs sampler is devised to help in exploring adaptive training samples which feature typical rare outage events. Interestingly, the originators engendering extreme spinning reserve inadequacy events can be traced using the sampling information of the proposed method. The performance of the proposed method is tested in an updated RTS-79 system vis-à-vis several existing methods. Spinning reserve inadequacy risk tracing is explained by uncovering a scenario frequency distribution concerning the short-term expected energy not supplied. INTRODUCTIONNowadays, the power systems have evolved to be an indispensable facility of great complexity to support civil life and social development. The increasing complexity primarily intended to be adapted for customer needs and electric markets and newly adopted techniques etc., commonly endows the contemporary power systems with basic defensive abilities against regional credible contingencies. However, we have already witnessed grave blackout consequences of complex power systems initiated by unpredictable rare contingencies, for example equipment decay or human-produced or natural hazards [1]. One recognised reason for spawning the observed rare initiators successful evolving into blackout essentially comes down to the lack of awareness of flexible operating reserve backing up very rare supply deficit.Operating reserve planning accounting for probabilistic factors can be traced back to 1963 [2], and since that period, the literature has documented several operating reserve planning schemes to economically hedging against outage risk, especially for renewable energy systems in recent passing years [3][4][5][6][7][8].This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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A partially collapsed Gibbs sampler with accelerated convergence for EEG source localization

Cited by 2 publications

References 12 publications

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

Tracing spinning reserve inadequacy risk via hybrid importance sampling with an optimised partially collapsed Gibbs sampler

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