Irreversible samplers from jump and continuous Markov processes

Ma, Yuanlin; Fox, Emily B.; Chen, Tianqi; Wu, Lei

doi:10.1007/s11222-018-9802-x

Cited by 21 publications

(38 citation statements)

References 69 publications

(162 reference statements)

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“…Like with the gradients, one can employ a proxy model to calculate an approximate FI matrix. The MCMC approaches using the curvature information are known in the literature [15,24,25,28], but are beyond the scope of this paper.…”

Section: Discussionmentioning

confidence: 99%

Applying kriging proxies for Markov chain Monte Carlo in reservoir simulation

2020

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One way to quantify the uncertainty in Bayesian inverse problems arising in the engineering domain is to generate samples from the posterior distribution using Markov chain Monte Carlo (MCMC) algorithms. The basic MCMC methods tend to explore the parameter space slowly, which makes them inefficient for practical problems. On the other hand, enhanced MCMC approaches, like Hamiltonian Monte Carlo (HMC), require the gradients from the physical problem simulator, which are often not available. In this case, a feasible option is to use the gradient approximations provided by the surrogate (proxy) models built on the simulator output. In this paper, we consider proxy-aided HMC employing the Gaussian process (kriging) emulator. We overview in detail the different aspects of kriging proxies, the underlying principles of the HMC sampler and its interaction with the proxy model. The proxy-aided HMC algorithm is thoroughly tested in different settings, and applied to three case studies-one toy problem, and two synthetic reservoir simulation models. We address the question of how the sampler performance is affected by the increase of the problem dimension, the use of the gradients in proxy training, the use of proxy-for-the-data and the different approaches to the design points selection. It turns out that applying the proxy model with HMC sampler may be beneficial for relatively small physical models, with around 20 unknown parameters. Such a sampler is shown to outperform both the basic Random Walk Metropolis algorithm, and the HMC algorithm fed by the exact simulator gradients.

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Section: Discussionmentioning

confidence: 99%

Applying kriging proxies for Markov chain Monte Carlo in reservoir simulation

2020

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“…We next demonstrate the performance of boosting with the FKL on a distribution with a large number of well-separated modes. We set as the target distribution a 2-dimensional Gaussian mixture model (GMM) with 20 components, previously used by Ma et al [2019].…”

Section: Simulation 2: Well-separated Modesmentioning

confidence: 99%

“…Figure 4: Log residual (log p/q k ) plots of for FKL boosting on a 2-dimensional GMM of 20 components [Ma et al, 2019].…”

Section: Real Data Experimentsmentioning

confidence: 99%

Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence

Jerfel,

Wang,

Fannjiang

et al. 2021

Preprint

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Variational Inference (VI) is a popular alternative to asymptotically exact sampling in Bayesian inference. Its main workhorse is optimization over a reverse Kullback-Leibler divergence (RKL), which typically underestimates the tail of the posterior leading to miscalibration and potential degeneracy. Importance sampling (IS), on the other hand, is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures. The quality of IS crucially depends on the choice of the proposal distribution. Ideally, the proposal distribution has heavier tails than the target, which is rarely achievable by minimizing the RKL. We thus propose a novel combination of optimization and sampling techniques for approximate Bayesian inference by constructing an IS proposal distribution through the minimization of a forward KL (FKL) divergence. This approach guarantees asymptotic consistency and a fast convergence towards both the optimal IS estimator and the optimal variational approximation. We empirically demonstrate on real data that our method is competitive with variational boosting and MCMC.

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“…To compare efficiency of the algorithms we compute a normalised effective sample size (nESS), where the normalisation is by the number of samples N . Following [6], we define the Effective Sample Size ESS = N/τ int where N is the number of steps of the chain (after appropriate burn-in) and τ int is the integrated autocorrelation time, τ int := 1 + k γ(k), where γ(k) is the lag − k autocorrelation. Consistently, the normalised ESS, nESS, is just nESS := ESS/N .…”

Section: Numerics: Sampling From Measures Supported On Bounded Domainsmentioning

confidence: 99%

“…Notice that nESS can be bigger than one (when the samples are negatively correlated), and this is something that will appear in our simulations. As an estimator for τ int we will take the Bartlett window estimator (see for example [6,Section 6], and references therein) rather than the initial monotone sequence estimator (see again [6,Section 6]), as the former is more suited to include non-reversible chains. Since the nESS is itself a random quantity, we performed 10 runs of each case using different seeds, and our plots below show P10, P50, P90 percentiles of the nESS from these runs.…”

Section: Numerics: Sampling From Measures Supported On Bounded Domainsmentioning

confidence: 99%

Reversible and non-reversible Markov chain Monte Carlo algorithms for reservoir simulation problems

2020

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We compare numerically the performance of reversible and non-reversible Markov Chain Monte Carlo algorithms for high dimensional oil reservoir problems; because of the nature of the problem at hand, the target measures from which we sample are supported on bounded domains. We compare two strategies to deal with bounded domains, namely reflecting proposals off the boundary and rejecting them when they fall outside of the domain. We observe that for complex high dimensional problems reflection mechanisms outperform rejection approaches and that the advantage of introducing non-reversibility in the Markov Chain employed for sampling is more and more visible as the dimension of the parameter space increases.

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Irreversible samplers from jump and continuous Markov processes

Cited by 21 publications

References 69 publications

Applying kriging proxies for Markov chain Monte Carlo in reservoir simulation

Applying kriging proxies for Markov chain Monte Carlo in reservoir simulation

Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence

Reversible and non-reversible Markov chain Monte Carlo algorithms for reservoir simulation problems

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