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Bayes Sensitivity with Fisher-Rao Metric [article]

Sebastian Kurtek, Karthik Bharath
2014 arXiv   pre-print
The approach is based on the square-root representation of densities which enables one to compute geodesics and geodesic distances in analytical form, facilitating the definition of naturally calibrated  ...  While the framework is general in spirit, the focus of this article is restricted to metric-based diagnosis under two settings: assessing local and global robustness in Bayesian procedures to perturbations  ...  When the baseline posterior mean is close to zero, the geometric and linear contamination methods result in similar values of the contaminated posterior mean (difference < 0.02).  ... 
arXiv:1403.5150v2 fatcat:uzslpsdjy5cuni5gug4foz6sbu

Bayesian sensitivity analysis with the Fisher–Rao metric

Sebastian Kurtek, Karthik Bharath
2015 Biometrika  
While the framework is general, the focus of this article is on assessing local and global robustness in Bayesian procedures to perturbations of the likelihood and prior, and identification of influential  ...  The approach is based on a square-root representation of densities, which enables analytic computation of geodesic paths and distances, facilitating the definition of naturally calibrated local and global  ...  distances with comparisons to the Kullback-Leibler divergence, additional examples for global/local sensitivity analysis and identification of influential observations, and proofs of propositions.  ... 
doi:10.1093/biomet/asv026 fatcat:tuaknri7jje57dcb5qzehqvnvi

Data Privacy Preservation Using Various Perturbation Techniques

Kavitha S , Raja vadhana P
2015 International Journal of Innovative Research in Computer and Communication Engineering  
It decreases the computation and communication cost in terms of time.  ...  The types are mainly classified into three types. 1) Rotation Perturbation In this method the value of the two attributes in the matrix are rotated but the meaning of the value is protected.  ... 
doi:10.15680/ijircce.2015.0302046 fatcat:s6b6g5zvtjf3tnnwxuyxqguri4

Perturbation Functions for Compact Database

Sergey I Vyatkin
2017 Review of Computer Engineering Research  
Article History Keywords Perturbation functions Geometric objects Geometric operations Relations Interactive object modeling Visualization. 3D Objects based on perturbation functions are considered in  ...  Symbolic computations required to produce a formula for the implicit form.  ...  INTERACTIVE GEOMETRIC MODELLING BASED ON THE PERTURBATION FUNCTIONS Creating models one of the main problems of modern computer graphics.  ... 
doi:10.18488/journal.76.2017.41.30.37 fatcat:uhloeji2lrdwziszuryxev6fse

Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models [article]

Abhijoy Saha, Sebastian Kurtek
2018 Sankhya A   pre-print
To quantify the different effects of the perturbations of the parameters and hyperparameters in these models on the posterior, we define three geometrically-motivated global sensitivity measures based  ...  on geodesic paths and distances computed under the nonparametric Fisher-Rao Riemannian metric on the space of densities, applied to posterior samples of densities: (1) the Fisher-Rao distance between density  ...  The authors would like to thank Karthik Bharath for valuable discussions and suggestions. SK was partially supported by NSF DMS 1613054, NSF CCF 1740761 and NIH R01-CA214955.  ... 
doi:10.1007/s13171-018-0145-7 pmid:34054249 pmcid:PMC8157310 arXiv:1810.03671v1 fatcat:ccbq243tc5fu7o4xu6fg27peue

Spin bath interaction effects on the geometric phase

Paula I. Villar
2009 Physics Letters A  
We show the dependence upon the system's and bath's parameter and analyze the range of validity of the perturbative approximation. Finally, we discuss the implications of our results.  ...  We calculate the geometric phase of a spin-1/2 particle coupled to an external environment comprising N spin-1/2 particle in the framework of open quantum systems.  ...  GEOMETRIC PHASE ENVIRONMENTALLY CORRECTED In this section, we shall compute the geometric phase for the central spin and analyze its deviation from the unitary geometric phase for a spin-1/2 particle.  ... 
doi:10.1016/j.physleta.2008.11.038 fatcat:iuuj3c5povc6hjeg3fprlusise

A Perturbation Method for the $T-\Omega$ Geometric Eddy-Current Formulation

Lorenzo Codecasa, Patrick Dular, Ruben Specogna, Francesco Trevisan
2010 IEEE transactions on magnetics  
The proposed formulation is applied to the feasibility design of a nondestructive evaluation device suitable to detect "long" longitudinal flaws in hot steel bars.  ...  A perturbation method for the geometric formulation to solve eddy-current problems is introduced.  ...  and in the undefected one , by means of the discrete perturbation method, Fig. 5 .  ... 
doi:10.1109/tmag.2010.2043932 fatcat:5v3u4o54jjddxbunk4lf6xnpue

Robust Geometric Computation [chapter]

Chee K. Yap, Vikram Sharma
2008 Encyclopedia of Algorithms  
By an L-bit input, we mean each of the numerical parameters in the description of the geometric object (see Section 35.2) is an L-bit number.  ...  THE NATURE OF GEOMETRIC COMPUTATION If the root cause of numerical nonrobustness is arithmetic, then it may appear that the problem can be solved with the right kind of arithmetic package.  ... 
doi:10.1007/978-0-387-30162-4_349 fatcat:h3xf7abcyzdazhvqpwszvkd7ca

The unequal-time matter power spectrum: impact on weak lensing observables [article]

Lucia F. de la Bella and Nicolas Tessore and Sarah Bridle
2021 arXiv   pre-print
Then we compute the angular power spectrum using a range of approaches: the Limber's approximation, and the geometric and midpoint approximations.  ...  We derive the unequal-time matter power spectrum at one-loop in standard perturbation theory and effective field theory to deal with non-linear physics.  ...  The work reported in this paper has been supported by the European Research Council in the form of a Consolidator Grant with Grant Agreement No. 681431 (LFdlB, NT, SB).  ... 
arXiv:2011.06185v3 fatcat:ygrlyfbjkbe3jibrptskejrwm4

Assessing Indices Tracking Changes in River Geochemistry and Implications for Monitoring

Caterina Gozzi, Antonella Buccianti
2022 Natural Resources Research  
Under this latter condition, the geometric mean of the composition shows a close connection with the cumulative sum of unclosed perturbation factors.  ...  To reach this goal, source-to-sink chemical changes in water and stream sediment composition of the Tiber river (central Italy) are analyzed using three indices: (i) the cumulative sum of unclosed perturbation  ...  The University of Florence is acknowledged for the financial assistance through University funds (A.B). Prof. Gerd Rantitsch, Prof. Orlando Vaselli and Dr.  ... 
doi:10.1007/s11053-022-10014-1 fatcat:5jjliku7ezcyleag6xukdwpote

Attack to Explain Deep Representation

Mohammad A. A. K. Jalwana, Naveed Akhtar, Mohammed Bennamoun, Ajmal Mian
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
The visually appealing results across these applications demonstrate the utility of our attack (and perturbations in general) beyond model fooling.  ...  The accumulated signal gradually manifests itself as a collection of visually salient features of the target label (in model fooling), casting adversarial perturbations as primitive features of the target  ...  Rather, it places adversarial perturbations as human-meaningful geometric features of the target label, albeit in a primitive and subtle form.  ... 
doi:10.1109/cvpr42600.2020.00956 dblp:conf/cvpr/JalwanaABM20 fatcat:46iqdhvcuvgjfe3q5gls47zizq

Degeneracy and Instability in Geometric Computation [chapter]

Kokichi Sugihara
2001 Geometric Modelling  
This paper describes main sources of instability in geometric computation, and reviews two mutually opposite approaches to this problem.  ...  Instability in geometric computation comes from numerical errors, which first cause misjudgements of geometric structure, and then generate topological inconsistency.  ...  This means that we can avoid any of the degenerate cases. This is the principle of the symbolic perturbation, and this enables us to concentrate on the implementation for the general case. 2.  ... 
doi:10.1007/978-0-387-35490-3_1 fatcat:mllkwvn7ibf7rkptzgrje5t4ha

Reduced Order Modeling of a Bladed Rotor with Geometric Mistuning: Alternative Bases and Extremely Large Mistuning

Yasharth Bhartiya, Alok Sinha
2013 International journal of gas turbine, propulsion and power systems  
In the earlier papers ((Sinha, 2009), (Sinha and Bhartiya, 2010) and (Bhartiya and Sinha, 2011a, b)), bases for MMDA have been formed using the mode shapes of cyclic sectors perturbed along the POD features  ...  The bases vectors for model reduction in MMDA have been formed using the mode shapes of cyclic sectors with blades' geometries perturbed along the POD (Proper Orthogonal Decomposition) features.  ...  The findings, opinions and recommendations expressed therein are those of the authors and are not necessarily those of Duke University or the AFRL or the GUIde Consortium Members.  ... 
doi:10.38036/jgpp.5.1_1 fatcat:z7sx4jfrvnbjdmwxxoqxn6r3za

A Model for Gaussian Perturbations of Graphene

C. T. J. Dodson
2015 Journal of statistical physics  
This would allow the representation of a trajectory of states under a given ambient or process change, so opening the possibility for geometrically formulated dynamical models to link structural perturbations  ...  However, its structure experiences perturbations in the presence of external influences, whether from substrate properties, thermal or electromagnetic fields, or ambient fluid movement.  ...  Acknowledgement The author is grateful to an anonymous reviewer who made the points addressed in the Remark on the second page.  ... 
doi:10.1007/s10955-015-1362-2 fatcat:f66zq6rs5ngs7fxmknsrgfeszu

Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method

Qian Zhang, Shenren Xu, Xianjun Yu, Jiaxin Liu, Dingxi Wang, Xiuquan Huang
2021 Chinese Journal of Aeronautics  
Existing alternatives to the MC-CFD, such as surrogate models and second-order derivatives based on the adjoint method, can greatly reduce the computational cost.  ...  In this work, an improved method is proposed to circumvent the low-accuracy problem of the MC-adj-linear without incurring the high cost of other alternative models.  ...  Acknowledgments The research is funded by the National Natural Science Foundation of China (No. 52006177) and National Science and Technology Major Project, China (No. 2017-II-0009-0023).  ... 
doi:10.1016/j.cja.2021.06.007 fatcat:fb5vbk6m25aafj2f63ccouk75q
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