Majorize–Minimize Adapted Metropolis–Hastings Algorithm

Marnissi, Yosra; Chouzenoux, Émilie; Benazza-Benyahia, Amel; Pesquet, Jean-Christophe

doi:10.1109/tsp.2020.2983150

Cited by 19 publications

(14 citation statements)

References 60 publications

(94 reference statements)

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“…In [44], the authors propose a TunaMH method based on MH (as its name evokes) for exposing a tunable tradeoff between its batch size and the convergence rate that is theoretically guaranteed. The authors of [45] propose a novel MH to provide large proposal transitions accepted with a high probability due to a significant increase in the complexity and in the dimension of the interference problems. The authors of [46] address the incipient fault detection problem, which is solved by the proposed two-step technique.…”

Section: Literature Reviewmentioning

confidence: 99%

Applicability of Generalized Metropolis-Hastings Algorithm to Estimating Aggregate Functions in Wireless Sensor Networks

Kenyeres¹,

Kenyeres²

2020

Adv. sci. technol. eng. syst. j.

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Over the last decades, numerous distributed consensus-based algorithms have found a wide application as a complementary mechanism for data aggregation in wireless sensor networks. In this paper, we provide an analysis of the generalized Metropolis-Hastings algorithm for data aggregation with a fully-distributed stopping criterion. The goal of the implemented stopping criterion is to effectively bound the algorithm execution over wireless sensor networks. In this paper, we analyze and compare the performance of the mentioned algorithm with various mixing parameters for distributed averaging, for distributed summing, and for distributed graph order estimation. The algorithm is examined under different configurations of the implemented stopping criterion over random geometric graphs by applying two metrics, namely the mean square error and the number of the iterations for the consensus. The goal of this paper is to examine the applicability of the analyzed algorithm with the stopping criterion to estimating the investigated aggregate functions in wireless sensor networks. In addition, the performance of the algorithm is compared to the average consensus algorithm bounded by the same stopping criterion.

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Section: Literature Reviewmentioning

confidence: 99%

Applicability of Generalized Metropolis-Hastings Algorithm to Estimating Aggregate Functions in Wireless Sensor Networks

Kenyeres¹,

Kenyeres²

2020

Adv. sci. technol. eng. syst. j.

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“…where A(μ (t+1) n ) is an SDP matrix of R dx×dx . The scaled gradient term in (7) can be understood as a discretization of (5) under the assumption of a locally constant curvature [19]. Like in the ULA scheme (6), the covariance matrix of the proposal density is adapted according to…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…The advantage is that a sample arising from the proposal is more likely drawn from a highly probable region, which is beneficial to the acceptance rate. The performance of MALA can be improved by introducing in the drift term a scaling matrix depending on the current sample value, in order to adapt the proposal to the local structure of the target density [17,18,19]. Several strategies have been investigated for the construction of the scaling matrix in MALA, relying on second-order information [20,18], Fisher metric [17] or majorization-minimization strategy [19].…”

Section: Introductionmentioning

confidence: 99%

Langevin-based Strategy for Efficient Proposal Adaptation in Population Monte Carlo

Elvira

Chouzenoux²

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Population Monte Carlo (PMC) algorithms are a family of adaptive importance sampling (AIS) methods for approximating integrals in Bayesian inference. In this paper, we propose a novel PMC algorithm that combines recent advances in the AIS and the optimization literatures. In such a way, the proposal densities are adapted according to the past weighted samples via a local resampling that preserves the diversity, but we also exploit the geometry of the targeted distribution. A scaled Langevin strategy with Newton-based scaling metric is retained for this purpose, allowing to adapt jointly the means and the covariances of the proposals, without needing to tune any extra parameter. The performance of the proposed technique is clearly superior in two numerical examples at the cost of a reasonable computational complexity increment.

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“…Let γ > 0 and let Q ∈ S n be a preconditioning matrix used to accelerate the sampler [22]. Following [15], π(x) is approximated by…”

Section: Preconditioned P-ula a Notationmentioning

confidence: 99%

Preconditioned P-ULA for Joint Deconvolution-Segmentation of Ultrasound Images

Marie-Caroline

Kouamé

Chouzenoux

et al. 2019

IEEE Signal Process. Lett.

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Joint deconvolution and segmentation of ultrasound images is a challenging problem in medical imaging. By adopting a hierarchical Bayesian model, we propose an accelerated Markov chain Monte Carlo scheme where the tissue reflectivity function is sampled thanks to a recently introduced proximal unadjusted Langevin algorithm. This new approach is combined with a forward-backward step and a preconditioning strategy to accelerate the convergence, and with a method based on the majorizationminimization principle to solve the inner nonconvex minimization problems. As demonstrated in numerical experiments conducted on both simulated and in vivo ultrasound images, the proposed method provides high-quality restoration and segmentation results and is up to six times faster than an existing Hamiltonian Monte Carlo method.

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Majorize–Minimize Adapted Metropolis–Hastings Algorithm

Cited by 19 publications

References 60 publications

Applicability of Generalized Metropolis-Hastings Algorithm to Estimating Aggregate Functions in Wireless Sensor Networks

Applicability of Generalized Metropolis-Hastings Algorithm to Estimating Aggregate Functions in Wireless Sensor Networks

Langevin-based Strategy for Efficient Proposal Adaptation in Population Monte Carlo

Preconditioned P-ULA for Joint Deconvolution-Segmentation of Ultrasound Images

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