Invertible Particle-Flow-Based Sequential MCMC With Extension to Gaussian Mixture Noise Models

Li, Yunpeng; Pal, Soumyasundar; Coates, Mark

doi:10.1109/tsp.2019.2905816

Cited by 18 publications

(12 citation statements)

References 45 publications

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“…Reference [40] proposes to employ invertible particle flow methods to construct the first proposal distribution in the Composite MH Kernel and gave two conclusions: 1) the mapping involving 𝜂 𝑖 0 and 𝜂 𝑖 1 is invertible mapping; 2) 𝐶 is invertible and the determinant of 𝐶 is not zero. Thus, the first proposal distribution 𝑞 𝑡 ,1 (•) could be constructed by invertible particle flow mapping and follows equation (13):…”

Section: Invertible Particle Flowmentioning

confidence: 99%

The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

Han¹,

Nakamura²

2021

Preprint

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Particle filtering methods are widely applied in sequential state estimation within nonlinear non-Gaussian state space model. However, the traditional particle filtering methods suffer the weight degeneracy in the high-dimensional state space model. Currently, there are many methods to improve the performance of particle filtering in high-dimensional state space model. Among these, the more advanced method is to construct the Sequential Markov chain Monte Carlo (SMCMC) framework by implementing the Composite Metropolis-Hasting (MH) Kernel. In this paper, we proposed to discretize the Zig-Zag Sampler and apply the Zig-Zag Sampler in the refinement stage of the Composite MH Kernel within the SMCMC framework which is implemented the invertible particle flow in the joint draw stage. We evaluate the performance of proposed method through numerical experiments of the challenging complex high-dimensional filtering examples. Numerical experiments show that in highdimensional state estimation examples, the proposed method improves estimation accuracy and increases the acceptance ratio compared with state-of-the-art filtering methods.

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Section: Invertible Particle Flowmentioning

confidence: 99%

The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

Han¹,

Nakamura²

2021

Preprint

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“…Step 1 Generate a candidate sample set by MCMC algorithm [31]. According to the function U, the prediction uncertainty increases as the U value decreases.…”

Section: B a New Strategy Of Determining The Optimal Samplementioning

confidence: 99%

An Efficient Adaptive Reliability Analysis Method Based on Kriging and Weighted Average Misclassification Rate Improvement

et al. 2019

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In the past few years, the Kriging model based on the adaptive design of experiments (DoE) has attracted extensive attention in analyzing the reliability of structures involving time-consuming simulations or complicated implicit performance function. Although varieties of sampling strategies have been proposed, they update DoE mainly by selecting the sample at which its corresponding learning function value is the maximum or minimum. However, there are usually two drawbacks. First, the training samples in DoE are easily clustered or overlapped. Second, the existing strategies usually only consider the improvement of prediction accuracy at the new training sample rather than the accuracy improvement of the region near the new training sample. Unfortunately, these two drawbacks can cause some unnecessary performance function evaluations. Therefore, an efficient adaptive sampling strategy and reliability analysis algorithm based on Kriging model, weighted average misclassification rate, sampling uniformity and gradient of prediction uncertainty are proposed. Furthermore, an improved stopping criterion based on the relative error estimation of failure probability is also developed to further reduce iteration. Subsequently, two explicit examples from the literature are analyzed to verify the effectiveness and superiority of the proposed method. Finally, a truss structure subjected to six external loads is investigated to illustrate the feasibility of the proposed reliability analysis method in engineering applications.

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“…Novel training algorithms that aim for stability [21,23] and increased efficiency [15,20] are actively being developed. Markov Chain Monte Carlo (MCMC) methods have also been employed for fitting GMMs to account for input variation [12,26,36]. Tree-based methods have also been proposed for efficient inference in k-means [18,33].…”

Section: Introductionmentioning

confidence: 99%

A sampling-based approach for efficient clustering in large datasets

Exarchakis¹,

Oubari²,

Lenz³

2021

Preprint

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We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our contribution is substantially more efficient than k-means as it does not require an all to all comparison of data points and clusters. We show that the optimal solutions of our approximation are the same as in the exact solution. However, our approach is considerably more efficient at extracting these clusters compared to the state-of-the-art. We compare our approximation with the exact k-means and alternative approximation approaches on a series of standardised clustering tasks. For the evaluation, we consider the algorithmic complexity, including number of operations to convergence, and the stability of the results. An efficient open source implementation of the algorithm is provided in the "peregrine" software repository.* Corresponding Author.significant. Recent advances in approximate inference methods have allowed for training algorithms with convergence performance that is sub-linear to the number of clusters [15]. This is typically achieved by avoiding the comparison between datapoints and clusters that lie far away in feature space.

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Invertible Particle-Flow-Based Sequential MCMC With Extension to Gaussian Mixture Noise Models

Cited by 18 publications

References 45 publications

The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo

An Efficient Adaptive Reliability Analysis Method Based on Kriging and Weighted Average Misclassification Rate Improvement

A sampling-based approach for efficient clustering in large datasets

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