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Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation [article]

Xiaohao Cai, Marcelo Pereyra, Jason D. McEwen
2019 arXiv   pre-print
Analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems and problems with non-smooth objective functionals (e.g. sparsity-promoting priors).  ...  Our methods support non-smooth priors for inverse problems and can be scaled to high-dimensional settings.  ...  Quantifying this kind of uncertainty, particularly for high-dimensional problems, is very challenging. This is the main focus in this article.  ... 
arXiv:1811.02514v2 fatcat:gkx7ubytwrcp5iwssntgx273ue

Maximum-a-posteriori estimation with Bayesian confidence regions [article]

Marcelo Pereyra
2016 arXiv   pre-print
Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems.  ...  This paper presents a new general methodology for approximating Bayesian high-posterior-density credibility regions in inverse problems that are convex and potentially very high-dimensional.  ...  As a result, most high-dimensional inference methods do not quantify uncertainty.  ... 
arXiv:1602.08590v3 fatcat:j2yvdwp53zgqlbhfv7gkkzggxm

Quantification of non-homogeneous interval uncertainty based on scatter in modal properties

Matthias Faes, David Moens
2017 Procedia Engineering  
The principal idea is to find a solution to an inverse problem, where the variability on the output side of the model (i.e., the eigenfrequencies) is known from measurement data, but the spatial uncertainty  ...  The principal idea is to find a solution to an inverse problem, where the variability on the output side of the model (i.e., the eigenfrequencies) is known from measurement data, but the spatial uncertainty  ...  This is done by solving the optimisation problem, as introduced in eq. (9) by means of a sequential quadratic programming algorithm, as explained in [8] , which converged after 25 iterations.  ... 
doi:10.1016/j.proeng.2017.09.251 fatcat:v5etv5dlrbauplk5njbttbqji4

Inverse Interval Field Quantification via Digital Image Correlation

Matthias Faes, David Moens
2018 Applied Mechanics and Materials  
via Digital Image Correlation, are applied in conjunction with a quasi-static finite element model.To apply these high-dimensional but scarce data, extensions to the novel method are introduced.A case  ...  study, investigating spatial uncertainty in Young's modulus of PA-12 parts, produced via Laser Sintering, shows that an accurate quantification of the constituting uncertainty is possible, albeit being  ...  Acknowledgements The authors would like to acknowledge support of the Flemish Research Foundation (FWO) in the framework of the project "HiDIF: High Dimensional Interval Fields" (project number G0C2218N  ... 
doi:10.4028/www.scientific.net/amm.885.304 fatcat:2adsndu4sjfe5hgzexwn63lqaa

Uncertainty quantification for radio interferometric imaging: II. MAP estimation

Xiaohao Cai, Marcelo Pereyra, Jason D McEwen
2018 Monthly notices of the Royal Astronomical Society  
by convex optimisation.  ...  Exploiting recent developments in the theory of probability concentration, we quantify uncertainties by post-processing the recovered MAP estimate.  ...  ACKNOWLEDGEMENTS This work is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) by grant EP/M011089/1, and Science and Technology Facilities Council (STFC) ST/M00113X/1.  ... 
doi:10.1093/mnras/sty2015 fatcat:ejyeu324gvczfpetncqwpirgau

Comparison of Bayesian and interval uncertainty quantification: Application to the AIRMOD test structure

Matteo Broggi, Matthias Faes, Edoardo Patelli, Yves Govers, David Moens, Michael Beer
2017 2017 IEEE Symposium Series on Computational Intelligence (SSCI)  
Since computational cost of the application of both methods to high-dimensional problems and realistic numerical models can become intractable, an Artificial Neural Network surrogate is used for both methods  ...  The comparison is made by applying both methods to the AIRMOD measurement data set, and comparing their results critically in terms of obtained information and computational expense.  ...  The interval vector θ I, * if input parameters is finally determined as : θ I, * =argmin δ(θ I ) s.t. θ I ∈ F I (12) Since the optimisation problem, introduced in eq. (10) is high dimensional and generally  ... 
doi:10.1109/ssci.2017.8280882 dblp:conf/ssci/BroggiFPGMB17 fatcat:5pla5xek6jczxh6rzlbbrcp4cq

Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau [article]

Alain Durmus, Eric Moulines, Marcelo Pereyra
2016 arXiv   pre-print
In addition to scaling efficiently to high dimensions, the method is straightforward to apply to models that are currently solved by using proximal optimisation algorithms.  ...  Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional image models and delivers accurate point estimation results.  ...  In this paper we focus on inverse problems that are convex.  ... 
arXiv:1612.07471v1 fatcat:5yhkbbe6qzev3hl5gox7obftu4

Heuristic linear algebraic rank-variance formulation and solution approach for efficient sensor placement

Younghwan Chae, Daniel N. Wilke
2017 Engineering structures  
In this study, we aim to improve the information available to solve an inverse problem by considering the optimal selection of m sensors from k options.  ...  The ability to solve an inverse problem depends on the quality of the optimisation approach and the relevance of information used to solve the inverse problem.  ...  Optimum sensor placement for localization in three dimensional under log normal shadowing. 2012 5th International Congress on Image and Signal Processing.  ... 
doi:10.1016/j.engstruct.2017.10.055 fatcat:vvmbqow7krepzhoccabfroimay

Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization [article]

Audrey Repetti, Marcelo Pereyra, Yves Wiaux
2018 arXiv   pre-print
We propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems.  ...  Computing such tests for imaging problems is generally very difficult because of the high dimensionality involved.  ...  Conclusions In this paper, we proposed a Bayesian uncertainty quantification methodology in the context of high dimensional imaging inverse problems.  ... 
arXiv:1803.00889v2 fatcat:y4oh4kcpknfhdelw5mixhwpjpq

A Framework for Optimization under Limited Information

Tansu Alpcan
2011 Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools  
In many real world problems, optimisation decisions have to be made with limited information.  ...  Explicitly quantifying the observations at each optimisation step using the entropy measure from information theory, the -often nonconvex-objective function to be optimised is modelled and estimated by  ...  A precursor to this paper "A framework for optimisation under limited information," by the same author has been published in the 5th Intl.  ... 
doi:10.4108/icst.valuetools.2011.245775 dblp:conf/valuetools/Alpcan11 fatcat:gqhebxcbcnfnzdeqpazimbzfaa

Multi-product pricing via robust optimisation

Aurélie Thiele
2008 Journal of Revenue and Pricing Management  
We derive robust counterparts to the deterministic pricing problem in the case of additive uncertainty, and analyse the impact of uncertainty and risk aversion on the decision-maker's strategy.  ...  We propose an approach to model demand uncertainty in pricing problems with capacitated resources that builds upon: (i) range forecasts for various product lines and (ii) bounds on the amount of the resources  ...  When there is no uncertainty, the problem of finding the optimal demand to maximise revenue is formulated as a quasi-convex (convex if the revenue is concave) programming problem with linear constraints  ... 
doi:10.1057/rpm.2008.41 fatcat:regeertdfvaupekpknxpo7mfd4

A framework for optimization under limited information

Tansu Alpcan
2012 Journal of Global Optimization  
In many real world problems, optimisation decisions have to be made with limited information.  ...  Explicitly quantifying the observations at each optimisation step using the entropy measure from information theory, the -often nonconvex-objective function to be optimised is modelled and estimated by  ...  A precursor to this paper "A framework for optimisation under limited information," by the same author has been published in the 5th Intl.  ... 
doi:10.1007/s10898-012-9942-z fatcat:7uvejmaqjzgvblqaw6jlueq53a

Simulated polyhedral clouds in robust optimisation

Martin Fuchs
2012 International Journal of Reliability and Safety  
Past studies of uncertainty handling with polyhedral clouds have already shown strength in dealing with higher dimensional uncertainties in robust optimisation, even in case of partial ignorance of statistical  ...  However, the number of function evaluations necessary to quantify and propagate the uncertainties has been too high to be useful in many real-life applications with respect to limitations of computational  ...  Partial support by the Fondation de Recherche pour l'Aéronautique et l'Espace (FRAE) in the framework of the project MEMORIA is gratefully appreciated.  ... 
doi:10.1504/ijrs.2012.044298 fatcat:ktkxmdemxnhtpayekpsfeb5fua

Uncertainty quantification for radio interferometric imaging – I. Proximal MCMC methods

Xiaohao Cai, Marcelo Pereyra, Jason D McEwen
2018 Monthly notices of the Royal Astronomical Society  
Since radio interferometric imaging requires solving a high-dimensional, ill-posed inverse problem, uncertainty quantification is difficult but also critical to the accurate scientific interpretation of  ...  However, traditional high-dimensional sampling methods are generally limited to smooth (e.g. Gaussian) priors and cannot be used with sparsity-promoting priors.  ...  ACKNOWLEDGEMENTS This work is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) by grant EP/M011089/1, and Science and Technology Facilities Council (STFC) ST/M00113X/1.  ... 
doi:10.1093/mnras/sty2004 fatcat:rued6sz2tvhs3iisb52pgqluly

Quantifying Model Uncertainty in Inverse Problems via Bayesian Deep Gradient Descent

Riccardo Barbano, Chen Zhang, Simon Arridge, Bangti Jin
2021 2020 25th International Conference on Pattern Recognition (ICPR)  
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks.  ...  In this work, we develop a scalable, data-driven, knowledge-aided computational framework to quantify the model uncertainty via Bayesian neural networks.  ...  RB is supported by a PhD studentship through the EPSRC Centre for Doctoral Training in Intelligent, Integrated Imaging In Healthcare (i4health) (EP/S021930/1), CZ is supported by a UCL Computer Science  ... 
doi:10.1109/icpr48806.2021.9412521 fatcat:ve3qklxphzhclm62guke4a5gvq
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