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Comparison of Accuracy for Methods to Approximate Fisher Information in the Scalar Case [article]

Shenghan Guo
2015 arXiv   pre-print
In such cases, we need to utilize the approximation of FIM. In general, there are two ways to estimate FIM.  ...  In this paper we mainly focus on the case where the unknown parameter that needs to be estimated by MLE is scalar and the random variables we have are independent.  ...  comparison of accuracy for the two approximation methods in the scalar case and mainly focused our analysis on the family of symmetric density functions.  ... 
arXiv:1501.00218v3 fatcat:4i7q5xcbkzaclkylwjlxsal2m4

M-FAC: Efficient Matrix-Free Approximations of Second-Order Information [article]

Elias Frantar, Eldar Kurtic, Dan Alistarh
2021 arXiv   pre-print
as in the classic approximation of the Hessian by the empirical Fisher matrix.  ...  In this work, we investigate matrix-free, linear-time approaches for estimating Inverse-Hessian Vector Products (IHVPs) for the case when the Hessian can be approximated as a sum of rank-one matrices,  ...  M-FAC outperforms previous methods in the case of MobileNetV1-STR by more than 1.5% Top-1 accuracy.  ... 
arXiv:2107.03356v5 fatcat:qmvcglffezcrbcfqy26z2q3dhi

Can We Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements?

G. H. Fisher, B. T. Welsch, W. P. Abbett
2011 Solar Physics  
The availability of vector magnetogram sequences with sufficient accuracy and cadence to estimate the time derivative of the magnetic field allows us to use Faraday's law to find an approximate solution  ...  Here, we show how additional information in the form of line-of-sight Doppler flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking  ...  The resulting solutions for E are shown in the third row of Figure 2 , with a scatterplot comparison of S z of the PTD method and the PTD plus Doppler information with the actual simulation electric fields  ... 
doi:10.1007/s11207-011-9816-4 fatcat:ptlk4rfglngo7cbfbwpnxdijue

Accelerated Experimental Design for Pairwise Comparisons [article]

Yuan Guo, Jennifer Dy, Deniz Erdogmus, Jayashree Kalpathy-Cramer, Susan Ostmo, J. Peter Campbell, Michael F. Chiang, Stratis Ioannidis
2019 arXiv   pre-print
This objective is known to perform well in practice, and is submodular, making the selection approximable via the greedy algorithm.  ...  When combined, the above improvements lead to an execution time of less than 1 hour for a dataset with 10^8 comparisons; the naïve greedy algorithm on the same dataset would require more than 10 days to  ...  For Mutual information we only execute it for batch size no more than 8, for Fisher information method we only execute it for batch size no more than 5.  ... 
arXiv:1901.06080v1 fatcat:bkt76v74nrgmbbc3jocft7i6tm

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation

Christoph Zimmer, Ramon Grima
2016 PLoS ONE  
The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.  ...  There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE).  ...  CZ would like to thank Ruth Großeholz for proofreading and helpful comments. CZ would also like to thank the two anonymous reviewers for their valuable comments.  ... 
doi:10.1371/journal.pone.0159902 pmid:27583802 pmcid:PMC5008843 fatcat:zamz4mgisfdkxe5sltzrxcc4oq

Microwave Background Constraints on Cosmological Parameters

Matias Zaldarriaga, David N. Spergel, Uroš Seljak
1997 Astrophysical Journal  
We use a high-accuracy computational code to investigate the precision with which cosmological parameters could be reconstructed by future cosmic microwave background (CMB) experiments, in particular the  ...  the ionization history of the universe.  ...  In §5, we explore the accuracy of the Fisher method by performing a more general type of analysis and investigate the effects of prior information in the accuracy of the reconstruction.  ... 
doi:10.1086/304692 fatcat:bt63oyyutjevbjxoqwastbmprm

Demonstration of Enhanced Monte Carlo Computation of the Fisher Information for Complex Problems [article]

Xumeng Cao
2014 arXiv   pre-print
The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest.  ...  We show through numerical examples how these methods improve the accuracy of the estimate of the information matrix compared to the basic resampling-based approach. Some relevant theory is summarized.  ...  T θ There are 5(5+1)/2 = 15 unique terms in F n (θ) that are to be estimated. The analytical form of the true Fisher information matrix is not attainable in this case.  ... 
arXiv:1405.1491v1 fatcat:krh5ky6zybbtdpiynx7rhdexeq

SVD (singular value decomposition) [chapter]

2008 Encyclopedia of Genetics, Genomics, Proteomics and Informatics  
A multi-level parameter estimation procedure is implemented to sequentially accumulate information from prior estimates in a Fisher information matrix for use in subsequent parameter estimates.  ...  The use of a generic uncertainty model in estimating the predictive accuracy of future DYNA simulations is enhanced through the use of a reduced set of principal component metrics and a basis augmentation  ...  The nonlinear finite element models used in the numerical example were developed by Karagozian & Case, Structural Engineers.  ... 
doi:10.1007/978-1-4020-6754-9_16446 fatcat:ndcr27p5ojdupg6m5qn6ihkda4

Fisher Information Field: an Efficient and Differentiable Map for Perception-aware Planning [article]

Zichao Zhang, Davide Scaramuzza
2020 arXiv   pre-print
To integrate the knowledge about localization accuracy in motion planning algorithms, a central task is to quantify the amount of information that an image taken at a 6 degree-of-freedom pose brings for  ...  To overcome these drawbacks, we propose the first dedicated map representation for evaluating the Fisher information of 6 degree-of-freedom visual localization for perception-aware motion planning.  ...  The maximum number of iterations was set to 100. The presented definition is the observed Fisher information. See [35] for the comparison of different concepts.  ... 
arXiv:2008.03324v1 fatcat:lmlmdm4irzdabie2k67pe3a3pu

Noise Properties of Motion-Compensated Tomographic Image Reconstruction Methods

Se Young Chun, Jeffrey A. Fessler
2013 IEEE Transactions on Medical Imaging  
Motion-compensated image reconstruction (MCIR) methods incorporate motion models to improve image quality in the presence of motion.  ...  MCIR methods differ in terms of how they use motion information and they have been well studied separately. However, there have been less theoretical comparisions of different MCIR methods.  ...  Acknowledgments This work was supported in part by NIH/NCI grant 1P01 CA87634.  ... 
doi:10.1109/tmi.2012.2206604 pmid:22759442 pmcid:PMC3821946 fatcat:64ix5olqyjdoxoqftmztm4wrva

WoodFisher: Efficient Second-Order Approximation for Neural Network Compression [article]

Sidak Pal Singh, Dan Alistarh
2020 arXiv   pre-print
Recently, there has been significant interest in utilizing this information in the context of deep neural networks; however, relatively little is known about the quality of existing approximations in this  ...  Further, even when iterative, gradual pruning is considered, our method results in a gain in test accuracy over the state-of-the-art approaches, for pruning popular neural networks (like ResNet-50, MobileNetV1  ...  Also, we would like to thank Alexander Shevchenko, Alexandra Peste, and other members of the group for fruitful discussions.  ... 
arXiv:2004.14340v5 fatcat:n2k7d354a5emxe4y5zewpotnh4

Spatially sensitive statistical shape analysis for pedestrian recognition from LIDAR data

Michalis A. Savelonas, Ioannis Pratikakis, Theoharis Theoharis, Georgios Thanellas, Frédéric Abad, Rémy Bendahan
2018 Computer Vision and Image Understanding  
This work introduces encoding methods for pedestrian recognition, based on statistical shape analysis of 3D LIDAR data.  ...  The latter method derives more detailed cues, by enriching the 'gross' information reflected by overall statistics of local shape descriptors, with 'fine-grained' information reflected by statistics associated  ...  For this reason and aiming 290 for clarity, we will only present recognition results from the SVM-based methods in the comparisons to follow.  ... 
doi:10.1016/j.cviu.2018.06.001 fatcat:xj5aa44r4fddvaaiaem5n43ztm

Parameter estimation and uncertainty quantification using information geometry [article]

Jesse A Sharp, Alexander P Browning, Kevin Burrage, Matthew J Simpson
2022 arXiv   pre-print
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic  ...  curves and Riemann scalar curvature, to supplement typical techniques for uncertainty quantification such as Bayesian methods, profile likelihood, asymptotic analysis and bootstrapping.  ...  Acknowledgements We thank Professor Alan Garfinkel (UCLA) for introducing K.B. to information geometry, and for numerous discussions while both were at the University of Oxford. We also thank Dr.  ... 
arXiv:2111.12201v3 fatcat:rqpho3wo3vdarprdlpqx6ahmwi

Accuracy of Measuring Camera Position by Marker Observation

Vladimir A. Grishin
2010 Journal of Software Engineering and Applications  
This bound justifies the specification of the CVS parameters and allows us to formulate constraints for an object trajectory based on required measurement accuracy.  ...  For making the measurement, the boundaries of marker image are used.  ...  In reference [11] , an expression of Fisher Information Matrix was derived for the case of one-dimensional signal.  ... 
doi:10.4236/jsea.2010.310107 fatcat:5sacr6xibjbinkfmfa23ey6azy

Page 6493 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
Multiple contrast tests which may be regarded as an approxima- tion of the generalized Bayes tests are obtained and their power comparisons are shown for the cases of k = 4, 5 and 6.  ...  Summary: “In the Bayesian approach, the Behrens-Fisher prob- lem has been posed as one of estimation for the difference of two means.  ... 
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