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Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation
[article]
2019
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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
2017
Procedia Engineering
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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
2018
Applied Mechanics and Materials
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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
2018
Monthly notices of the Royal Astronomical Society
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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
2017
2017 IEEE Symposium Series on Computational Intelligence (SSCI)
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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]
2016
arXiv
pre-print
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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
2017
Engineering structures
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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]
2018
arXiv
pre-print
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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
2011
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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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
2008
Journal of Revenue and Pricing Management
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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
2012
Journal of Global Optimization
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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
2012
International Journal of Reliability and Safety
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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
2018
Monthly notices of the Royal Astronomical Society
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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
2021
2020 25th International Conference on Pattern Recognition (ICPR)
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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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