Kennamer, Noble William · eScholarship (California Digital Library) · 2022
In this work we study variational methods for Bayesian optimal experimental design (BOED). Experimentation is a cornerstone of science and is central to any major engineering effort. Often experiments require the use of substantial resources, from expensive equipment to limited researcher time; in addition, experiments can be dangerous or may be required to be completed in a given period of time. For these reasons, we prefer to conduct our experiments as efficiently as possible, acquiring as much information as we can given the resources available to us. Optimal experimental design (OED) is a sub-field of statistics focused on developing methods for accomplishing this goal. The OED problem is formulated by defining a utility function over designs and optimizing this function over the set of all feasible designs. We focus on the \\emph{Expected Information Gain} (EIG), a widely used utility function with sound theoretical support. However, in practice the EIG is intractable to compute, and approximation strategies are required. We investigate the use of variational methods for this purpose and show substantial improvement over competing approximation techniques. A specific form of OED common in the field of machine learning (ML) is \\emph{active learning} (AL). In the active learning framework, we would like to obtain a labeled dataset in order to train a supervised model. However, for all the reasons stated, labeling data points can be costly and again we should make efficient use of our labeling resources. We present a novel application of active learning to optimize spectroscopic follow up for large scale astronomical surveys. Finally, much of this work requires learning functions over sets which we know must satisfy certain properties (e.g., permutation invariance). We conclude the thesis by presenting a novel neural network architecture for predicting the astronomical class of individual objects in the same exposure using a neural architecture specifically designed to accommodate known inductive biases present in the data.
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Dyvak Nikolai Petrovich · OpenGrey (Institut de l'Information Scientifique et Technique) · 1992
Method of analysing prediction characteristics and optimal concentrated experimental design applied in construction of interval object models are worked out. Models of interval errors are studied, algorithm of optimal step-to-step interval experimental design is developed. The procedure of interval data approach by splane functions is worked up. Optimal interval experimental design is developed, compression algorithm of grathical map data is obtained. Compression data algorithm is introduced into navigational system by means of digital maps of the terrain. Field of application: analysis and representation of mathematical object models for their effective control
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Manuel Higueras, Jesús López–Fidalgo · 2023
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Koerkel, S. · OpenGrey (Institut de l'Information Scientifique et Technique) · 2002
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Kenneth Lange, Michael Boehnke · Annals of Human Genetics · 1992
Radiation hybrid mapping is a somatic cell technique for ordering human loci along a chromosome and estimating the physical distance between adjacent loci. The present paper considers a realistic model of fragment generation and retention. This model assumes that fragments are generated in the ancestral cell of a clone according to a Poisson breakage process along the chromosome. Once generated, fragments are independently retained in the clone with a common retention probability. Based on this and less restrictive models, statistical criteria such as minimum obligate breaks, maximum likelihood, and Bayesian posterior probabilities can be used to decide order. Distances can be estimated by either maximum likelihood or Bayesian posterior means. The model also permits rational design of radiation dose for optimal statistical precision. A brief examination of some real data illustrates our criteria and computational algorithms.
Cited by 31Open access
Petrocchi, Andrea, Scharrer, Matthias K., Volkwein, Stefan · KOPS (University of Konstanz) · 2022
In this paper we propose an algorithm for the bi-level optimal experimental design involving a parameter-dependent evolution problems. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trust-region reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.
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Sarah Walsh, William Sealy, Karen M. Feigh · Advances in intelligent systems and computing · 2020
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Hainy, Markus Leopold · University Library Linz repository (Johannes Kepler Universitat Linz) · 2015
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Johannessen, Kristian John. · Monash University · 2022
This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
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Naiara Korta Martiartu, Christian Boehm, Václav Hapla et al. · The Journal of the Acoustical Society of America · 2019
Ultrasound computed tomography (USCT) is an emerging modality to image the acoustic properties of the breast tissue for cancer diagnosis. With the need of improving the diagnostic accuracy of USCT, while maintaining the cost low, recent research is mainly focused on improving (1) the reconstruction methods and (2) the acquisition systems. D-optimal sequential experimental design (D-SOED) offers a method to integrate these aspects into a common systematic framework. The transducer configuration is optimized to minimize the uncertainties in the estimated model parameters, and to reduce the time to solution by identifying redundancies in the data. This work presents a formulation to jointly optimize the experiment for transmission and reflection data and, in particular, to estimate the speed of sound and reflectivity of the tissue using either ray-based or wave-based imaging methods. Uncertainties in the parameters can be quantified by extracting properties of the posterior covariance operator, which is analytically computed by linearizing the forward problem with respect to the prior knowledge about parameters. D-SOED is first introduced by an illustrative toy example, and then applied to real data. This shows that the time to solution can be substantially reduced, without altering the final image, by selecting the most informative measurements.
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Joakim Beck, Ben Mansour Dia, Luis Espath et al. · International Journal for Numerical Methods in Engineering · 2020
Summary An optimal experimental set‐up maximizes the value of data for statistical inferences. The efficiency of strategies for finding optimal experimental set‐ups is particularly important for experiments that are time‐consuming or expensive to perform. In the situation when the experiments are modeled by partial differential equations (PDEs), multilevel methods have been proven to reduce the computational complexity of their single‐level counterparts when estimating expected values. For a setting where PDEs can model experiments, we propose two multilevel methods for estimating a popular criterion known as the expected information gain (EIG) in Bayesian optimal experimental design. We propose a multilevel double loop Monte Carlo, which is a multilevel strategy with double loop Monte Carlo, and a multilevel double loop stochastic collocation, which performs a high‐dimensional integration on sparse grids. For both methods, the Laplace approximation is used for importance sampling that significantly reduces the computational work of estimating inner expectations. The values of the method parameters are determined by minimizing the computational work, subject to satisfying the desired error tolerance. The efficiencies of the methods are demonstrated by estimating EIG for inference of the fiber orientation in composite laminate materials from an electrical impedance tomography experiment.
Cited by 4Open access
Joakim Beck, Ben Mansour Dia, Luis Espath et al. · arXiv (Cornell University) · 2018
An optimal experimental set-up maximizes the value of data for statistical\ninferences and predictions. The efficiency of strategies for finding optimal\nexperimental set-ups is particularly important for experiments that are\ntime-consuming or expensive to perform. For instance, in the situation when the\nexperiments are modeled by Partial Differential Equations (PDEs), multilevel\nmethods have been proven to dramatically reduce the computational complexity of\ntheir single-level counterparts when estimating expected values. For a setting\nwhere PDEs can model experiments, we propose two multilevel methods for\nestimating a popular design criterion known as the expected information gain in\nsimulation-based Bayesian optimal experimental design. The expected information\ngain criterion is of a nested expectation form, and only a handful of\nmultilevel methods have been proposed for problems of such form. We propose a\nMultilevel Double Loop Monte Carlo (MLDLMC), which is a multilevel strategy\nwith Double Loop Monte Carlo (DLMC), and a Multilevel Double Loop Stochastic\nCollocation (MLDLSC), which performs a high-dimensional integration by\ndeterministic quadrature on sparse grids. For both methods, the Laplace\napproximation is used for importance sampling that significantly reduces the\ncomputational work of estimating inner expectations. The optimal values of the\nmethod parameters are determined by minimizing the average computational work,\nsubject to satisfying the desired error tolerance. The computational\nefficiencies of the methods are demonstrated by estimating the expected\ninformation gain for Bayesian inference of the fiber orientation in composite\nlaminate materials from an electrical impedance tomography experiment. MLDLSC\nperforms better than MLDLMC when the regularity of the quantity of interest,\nwith respect to the additive noise and the unknown parameters, can be\nexploited.\n
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Tel'pukhov Vi, Shepelev Va, Lisenkov An · PubMed · 1982
An optimal variant of myocardial conservation was found by means of the methods of experimental design with the use of a small number of experiments. This variant consists of different regimens and conditions affecting the results of transplantation with the use of weak aldehyde concentrations. The conservation regimens in question allow more complete protection of the test organ against long-term ischemic injuries preserving myocardial contractility during the post-transplantation period.
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Tsae-yun Daphne Lin · 1984
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Xiaohong Wang, Fan Wen-hui, Lizhi Wang · 2018 1st IEEE International Conference on Knowledge Innovation and Invention (ICKII) · 2018
How to obtain the most effective experimental data under limited resources via the optimal experimental design is one of main research topics of Accelerating Degradation Test (ADT). At present, the research on ADT design method mainly focuses on design randomness, while the design fuzziness hasn't been widely discussed but is another critical uncertainty to be addressed included in all aspects of experiment design. This paper is proposing an ADT optimal design methodology based on fuzzy theory, including methods of fuzzy objective and constraints determination, result assessment, and optimal design procedures. An engineering case about rubber seal ring ADT experimental design is provided to validate optimal design methodology to address fuzzy problem and enhance ADT design.
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Paul J. Wissmann, Martha A. Grover · AIChE Journal · 2008
Abstract Empirical and mechanistic experimental design methods are combined to construct partial models, which are, thus, used to design a process. The grid algorithm restricts the next experimental point to potential process optima, according to the confidence intervals around the optimal points, and works with any experimental design algorithm such as D‐optimal. Two case studies show the advantages of implementing the grid algorithm. On average the improvement due to the grid algorithm was 15–20% in the first case study. The second case study is based on thin film growth using four potential models, with the most probable model used for experimental design. The grid algorithm balances the trade‐off between two extremes: D‐optimal designs and sampling at the predicted optimal point. The methodology presented shows that the experimenter does not have to decide ahead of time on purely empirical or mechanistic experimental design methods, since both may be useful. © 2008 American Institute of Chemical Engineers AIChE J, 2009
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Baijnath Kaushik, Haider Banka · International Journal of Advanced Intelligence Paradigms · 2014
This paper present an optimal artificial neural network approach for improving upper bound on link reliability in optimal network design. Improving reliability in a growing variable-sized network is an important parameter for optimal network design. Many alternative methods for improving reliability have been used for optimal network design. Most of these methods, mentioned in the literature are simulation-based. These methods provide simple ways for measuring reliability when networks have limited size. These methods require significant computational effort and time for growing variable-sized networks. An optimal neural network method is therefore proposed for reliability improvement in optimal network design. The proposed algorithm has two phases: experimental setup and optimal phase. Experimental setup phase scans all possible network topologies for reliability measures. And, optimal phase constructs optimal network design with improved reliability upper-bound. Both neural networks were studied with fixed and varying links. Results are grouped using cross-validation method showing that the optimised artificial neural network approach gives precise measures for significant reliability improvement than the upper-bound than heuristic-based approach. Results show that the optimised ANN produces optimal network designs and reliability measures at reasonable computational cost.
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Mohammad Ali Nikouei, M. Amiri · Journal of Operational Research and Its Applications · 2022
Application of Experimental Design Methods and Fuzzy Multi-Criteria Decision Making in The Determination of The Optimal Reliability of The Two-stage Assembly Flow Shop Scheduling System
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Henry C. Co · International Journal of Production Research · 2008
In Taguchi's methods of parameter design, a confirmation test is usually necessary to remove concerns about the choice of control parameters, experimental design, or assumptions about responses. This paper investigated the use of artificial neural-networks simulation to validate the set of control parameters identified as significant through Taguchi's methods, and to verify that the recommended settings for the control parameters are indeed optimal or near-optimal. Using the experimental layout and measured responses from a Taguchi parameter-design experiment, we applied cross-validate training to ascertain that the trained neural-network can reproduce acceptable results on unseen experimental layouts. We then used the trained neural-network to simulate and search for the global optimal settings for the control parameters, and the results compared with the recommended settings from the Taguchi parameter-design experiment.
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Akın Özdemir, Byung Rae Cho · Engineering Optimization · 2019
Finding optimum conditions for process factors in an engineering optimization problem with response surface functions requires structured data collection using experimental design. When the experimental design space is constrained owing to external factors, its design space may form an asymmetrical and irregular shape and thus standard experimental design methods become ineffective. Computer-generated optimal designs, such as D-optimal designs, provide alternatives. While several iterative exchange algorithms for D-optimal designs are available for a linearly constrained irregular design space, it has not been clearly understood how D-optimal design points need to be generated when the design space is nonlinearly constrained and how response surface models are optimized. This article proposes an algorithm for generating the D-optimal design points that satisfy both feasibility and optimality conditions by using piecewise linear functions on the design space. The D-optimality-based response surface design models are proposed and optimization procedures are then analysed.
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