Inference Given Summary Statistics

Najm, Habib N.; Chowdhary, Kenny

doi:10.1007/978-3-319-11259-6_68-1

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…In ABC methods it is common practice to summarize the measurements by socalled summary statistics in order to improve the efficiency of such algorithms, see e.g. [10,11]. However, the identification of proper summary statistics containing sufficient information for inference is a difficult task, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench

John¹,

Livia²,

Schillings³

et al. 2021

Preprint

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Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these uncertain inverse problems. Standard methods used to identify uncertain parameters are Markov Chain Monte Carlo (MCMC) methods with explicit evaluation of a likelihood function. However, if the likelihood is very complex, such that its evaluation is computationally expensive, or even unknown in its explicit form, Approximate Bayesian Computation (ABC) methods provide a promising alternative. In this work both methods are first applied to artificially generated data and second on a real world problem, by using data of an electric motor test bench. We show that both methods are able to infer the distribution of varying parameters with a Bayesian hierarchical approach. But the proposed ABC method is computationally much more efficient in order to achieve results with similar accuracy. We suggest to use summary statistics in order to reduce the dimension of the data which significantly increases the efficiency of the algorithm. Further the simulation model is replaced by a Polynomial Chaos Expansion (PCE) surrogate to speed up model evaluations. We proof consistency for the proposed surrogate-based ABC method with summary statistics under mild conditions on the (approximated) forward model.

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Section: Introductionmentioning

confidence: 99%

Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench

John¹,

Livia²,

Schillings³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The approach using the Kullback‐Leibler divergence has been used extensively over the last three decades for imposing constraints in the framework of learning with statistical models. Many developments and applications have been published such as, for instance, the following interesting papers devoted to the training of neural network classifiers, learning topological, ensemble learning related to multilayer networks, constraints on parameters during learning, recognition of human activities, text categorization, exploration of data analysis, classification problems with constrained data, statistical learning algorithms with linguistic constraints, reinforcement learning in finite Markov decision processes, visual recognition, optimal sequential allocation, identifiability of parameter learning machines, speech enhancement, the training of generative neural samplers, pessimistic uncertainty quantification problem, inference given summary statistics, optimization framework concerning distance metric learning unsupervised machine learning techniques to learn latent parameters, graph‐based semisupervised learning, speech enhancement, and finally, to the broad learning systems …”

Section: Introductionmentioning

confidence: 99%

Physics‐constrained non‐Gaussian probabilistic learning on manifolds

Soize

Ghanem

2019

Numerical Meth Engineering

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Summary An extension of the probabilistic learning on manifolds (PLoM), recently introduced by the authors, has been presented: In addition to the initial data set given for performing the probabilistic learning, constraints are given, which correspond to statistics of experiments or of physical models. We consider a non‐Gaussian random vector whose unknown probability distribution has to satisfy constraints. The method consists in constructing a generator using the PLoM and the classical Kullback‐Leibler minimum cross‐entropy principle. The resulting optimization problem is reformulated using Lagrange multipliers associated with the constraints. The optimal solution of the Lagrange multipliers is computed using an efficient iterative algorithm. At each iteration, the Markov chain Monte Carlo algorithm developed for the PLoM is used, consisting in solving an Itô stochastic differential equation that is projected on a diffusion‐maps basis. The method and the algorithm are efficient and allow the construction of probabilistic models for high‐dimensional problems from small initial data sets and for which an arbitrary number of constraints are specified. The first application is sufficiently simple in order to be easily reproduced. The second one is relative to a stochastic elliptic boundary value problem in high dimension.

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Inference Given Summary Statistics

Cited by 2 publications

References 22 publications

Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench

Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench

Physics‐constrained non‐Gaussian probabilistic learning on manifolds

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