Approximate variational inference based on a finite sample of Gaussian latent variables

Gianniotis, Nikolaos; Schnörr, Christoph; Molkenthin, Christian; Bora, Sanjay Singh

doi:10.1007/s10044-015-0496-9

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…This approach makes use of the same model augmentations utilised in this work. The variational posterior of the triggering parameters could be inferred, e.g., via blackbox variational inference (Ranganath et al 2014;Gianniotis et al 2015). Alternatively, one could restrict the calculations to finding the MAP estimate of the GP-ETAS model.…”

Section: Case Study: L'aquila Italymentioning

confidence: 99%

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

et al. 2022

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The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l’Aquila region, Italy, with the devastating event on 6 April 2009, is presented.

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Section: Case Study: L'aquila Italymentioning

confidence: 99%

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

et al. 2022

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“…The free parameters in (10) are µ, r and θ. Note the simplification in the entropy term due to the orthogonal…”

Section: Mean and Scaling Of Covariance -Mvi Eigmentioning

confidence: 99%

“…Following [6,10] we draw S number of samples z s ∼ N (0, I D ) which we keep fixed throughout the optimisation of the objectives in ( 8), ( 10) and (11). This enables the use of scaledconjugate gradients (SCG) as the optimisation routine [16] in contrast to the typically employed stochastic gradient descent 4 .…”

Section: Optimisationmentioning

confidence: 99%

“…An update of the variational parameters follows, typically using a small step size in a stochastic gradient descent setting, after which the D KL is approximated with a new Monte Carlo average. In a slightly manner, [6,10] fix the Monte Carlo average approximation of the D KL throughout the optimisation of the variational parameters. We finally note that often in practice e.g.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Variational Inference

Gianniotis

2019

2019 International Joint Conference on Neural Networks (IJCNN)

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The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies. Variational approaches avoid this issue by explicitly minimising the Kullback-Leibler divergence D KL between a postulated posterior and the true (unnormalised) logarithmic posterior. However, they rely on a closed form D KL in order to update the variational parameters. To address this, stochastic versions of variational inference have been devised that approximate the intractable D KL with a Monte Carlo average. This approximation allows calculating gradients with respect to the variational parameters. However, variational methods often postulate a factorised Gaussian approximating posterior. In doing so, they sacrifice a-posteriori correlations. In this work, we propose a method that combines the Laplace approximation with the variational approach. The advantages are that we maintain: applicability on non-conjugate models, posterior correlations and a reduced number of free variational parameters. Numerical experiments demonstrate improvement over the Laplace approximation and variational inference with factorised Gaussian posteriors.

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A Mathematical Deduction of Variational Minimum Distance in Gaussian Space and Its Possible Application to Artificial Intelligence

Anda-Suárez

Ortiz-Aguilar

Calzada-Ledesma

et al. 2022

Studies in Computational Intelligence

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Approximate variational inference based on a finite sample of Gaussian latent variables

Cited by 3 publications

References 15 publications

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

Mixed Variational Inference

A Mathematical Deduction of Variational Minimum Distance in Gaussian Space and Its Possible Application to Artificial Intelligence

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