Relevant bibliographies by topics / Fisher information matrix (FIM)

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Academic literature on the topic 'Fisher information matrix (FIM)'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Fisher information matrix (FIM)"

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Jagannatham, Aditya K., and Bhaskar D. Rao. "Fisher-Information-Matrix Based Analysis of Semiblind MIMO Frequency Selective Channel Estimation." ISRN Signal Processing 2011 (September 7, 2011): 1–13. http://dx.doi.org/10.5402/2011/758918.

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We present a study of semiblind (SB) estimation for a frequency-selective (FS) multiple-input multiple-output (MIMO) wireless channel using a novel Fisher-information matrix (FIM) based approach. The frequency selective MIMO system is modeled as a matrix finite impulse response (FIR) channel, and the transmitted data symbols comprise of a sequence of pilot symbols followed by the unknown blind symbols. It is demonstrated that the FIM for this system can be expressed as the sum of the blind FIM Jb and pilot FIM Jp. We present a key result relating the rank of the FIM to the number of blindly identifiable parameters. We then present a novel maximum-likelihood (ML) scheme for the semiblind estimation of the MIMO FIR channel. We derive the Cramer-Rao Bound (CRB) for the semiblind scheme. It is observed that the semi-blind MSE of estimation of the MIMO FIR channel is potentially much lower compared to an exclusively pilot-based scheme. Finally, we derive a lower bound for the minimum number of pilot symbols necessary for the estimation of an FIR MIMO channel for any general semi-blind scheme. Simulation results are presented to augment the above analysis.
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Karakida, Ryo, Shotaro Akaho, and Shun-ichi Amari. "Pathological Spectra of the Fisher Information Metric and Its Variants in Deep Neural Networks." Neural Computation 33, no. 8 (July 26, 2021): 2274–307. http://dx.doi.org/10.1162/neco_a_01411.

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The Fisher information matrix (FIM) plays an essential role in statistics and machine learning as a Riemannian metric tensor or a component of the Hessian matrix of loss functions. Focusing on the FIM and its variants in deep neural networks (DNNs), we reveal their characteristic scale dependence on the network width, depth, and sample size when the network has random weights and is sufficiently wide. This study covers two widely used FIMs for regression with linear output and for classification with softmax output. Both FIMs asymptotically show pathological eigenvalue spectra in the sense that a small number of eigenvalues become large outliers depending on the width or sample size, while the others are much smaller. It implies that the local shape of the parameter space or loss landscape is very sharp in a few specific directions while almost flat in the other directions. In particular, the softmax output disperses the outliers and makes a tail of the eigenvalue density spread from the bulk. We also show that pathological spectra appear in other variants of FIMs: one is the neural tangent kernel; another is a metric for the input signal and feature space that arises from feedforward signal propagation. Thus, we provide a unified perspective on the FIM and its variants that will lead to more quantitative understanding of learning in large-scale DNNs.
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Qin, Bo Ying, and Xian Kun Lin. "Optimal Sensor Placement Based on Particle Swarm Optimization." Advanced Materials Research 271-273 (July 2011): 1108–13. http://dx.doi.org/10.4028/www.scientific.net/amr.271-273.1108.

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In order to dispose sensors to reasonable freedom degrees, and reflect adequately the dynamic characteristics of tested structure, the sensor locations of dynamic testing must be optimized. In this paper, taking MAC matrix, Fisher information matrix (FIM), and their combinations as optimization criteria respectively, the particle swarm optimization (PSO) was applied to the optimal sensor location problem (OSLP). The effect of optimization criteria and optimal method to optimal sensor locations were discussed. According to the optimized results, we can arrived at the following conclusions: using MAC and FIM as optimal criteria, introducing the PSO into the OSLP, the optimal sensor locations can ensure the better linear independence of the mode shape vectors and the better estimation of the experimental modal parameters.
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Huang, Li Xin, Xiang Wu Guo, Bo Tao Du, Xiao Jun Zhou, and Yu Yin Liu. "Optimal Measurement Placement for Material Parameter Identification of Orthotropic Composites by the Finite Element Method." Applied Mechanics and Materials 94-96 (September 2011): 1723–28. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.1723.

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An algorithm of the optimal measurement placement is proposed for the material parameter identification of two-dimensional orthotropic composites, which is modeled by the finite element. From the analysis of the system sensitivity matrix of the parameter identification processes using the Levenberg-Marquardt method, A-optimality criterion related with the Fisher Information Matrix (FIM) is selected for the criterion of the optimal measurement placement. Thus, the algorithm for selecting the optimal measurement placement can be constructed. A numerical example is given to demonstrate the effectiveness of the proposed algorithm. The example reveals that the measurement placement has a significant influence on the identification results.
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Wang, Xuezhi, Branko Ristic, Braham Himed, and Bill Moran. "Trajectory Optimisation for Cooperative Target Tracking with Passive Mobile Sensors." Signals 2, no. 2 (April 7, 2021): 174–88. http://dx.doi.org/10.3390/signals2020014.

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The paper considers the problem of tracking a moving target using a pair of cooperative bearing-only mobile sensors. Sensor trajectory optimisation plays the central role in this problem, with the objective to minimize the estimation error of the target state. Two approximate closed-form statistical reward functions, referred to as the Expected Rényi information divergence (RID) and the Determinant of the Fisher Information Matrix (FIM), are analysed and discussed in the paper. Being available analytically, the two reward functions are fast to compute and therefore potentially useful for longer horizon sensor trajectory planning. The paper demonstrates, both numerically and from the information geometric viewpoint, that the Determinant of the FIM is a superior reward function. The problem with the Expected RID is that the approximation involved in its derivation significantly reduces the correlation between the target state estimates at two sensors, and consequently results in poorer performance.
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Gogolev, I. V., and G. Yu Yashin. "Statistical Characteristics of Signal Parameter Estimation by Normalized Correlation Function Maximization." Journal of the Russian Universities. Radioelectronics, no. 3 (July 19, 2018): 15–22. http://dx.doi.org/10.32603/1993-8985-2018-21-3-15-22.

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In this paper differences between Fisher Information Matrix (FIM) and inverse covariation matrix of normalized correlation estimations for white and colored noise are investigated. It’s shown that implementation of normalized correlation function estimation leads to modification of maximum likelihood estimation FIM elements, so in case of arbitrary energy affected parameter vector, variance of estimation by normalized correlation function maximization is not equal to Cramer–Rao lower bound. Statistical characteristics of joint Doppler stretch and delay estimation by maximization of normalized correlation function for signal with nuisance parameters are derived in this paper. It’s shown that normalized correlator is equal to wideband ambiguity function, but this method of estimation follows from Cauchy–Schwarz inequality without using energy conservation assumptions. Besides, it is proved that estimation of Doppler stretch and delay by normalized correlation function or WBAF of signal with random initial phase and gain is asymptotically unbiased and effective.
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Qin, Bo Ying, and Xian Kun Lin. "Application of Integer-Coded Genetic Algorithm to Optimal Sensor Placement." Advanced Materials Research 271-273 (July 2011): 1114–19. http://dx.doi.org/10.4028/www.scientific.net/amr.271-273.1114.

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In the dynamic testing, the sensor positions have a major influence on the quality of the experimental modal parameters of a tested structure. In order to dispose sensors to reasonable degrees of freedom (DOF), and reflect adequately the dynamic characteristics of tested structure, the sensor positions must be optimized. In this paper, taking the combination of MAC matrix and Fisher information matrix (FIM) as optimization criteria, the integer-coded genetic algorithm (IGA) was applied to optimal sensor position problem (OSPP). The effect of optimization criteria and optimal method to optimal sensor positions were discussed. According to the results, the following conclusion is obtained: using MAC and FIM as optimal criteria, introducing the IGA into the OSPP, the optimal sensor positions can ensure the better linear independence of the mode shape vectors and the better estimation of the experimental modal parameters. Comparing with three existing optimal sensor placement methods, which are Guyan, effective independence (EI), and cumulative method based on QR decomposition (CQRD), their results of the optimal sensor positions indicated that the IGA is better than them.
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Salah, Mukhtar M., Essam A. Ahmed, Ziyad A. Alhussain, Hanan Haj Ahmed, M. El-Morshedy, and M. S. Eliwa. "Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution." PLOS ONE 16, no. 1 (January 20, 2021): e0244316. http://dx.doi.org/10.1371/journal.pone.0244316.

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This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.
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Fox, Zachary R., Gregor Neuert, and Brian Munsky. "Optimal Design of Single-Cell Experiments within Temporally Fluctuating Environments." Complexity 2020 (June 13, 2020): 1–15. http://dx.doi.org/10.1155/2020/8536365.

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Modern biological experiments are becoming increasingly complex, and designing these experiments to yield the greatest possible quantitative insight is an open challenge. Increasingly, computational models of complex stochastic biological systems are being used to understand and predict biological behaviors or to infer biological parameters. Such quantitative analyses can also help to improve experiment designs for particular goals, such as to learn more about specific model mechanisms or to reduce prediction errors in certain situations. A classic approach to experiment design is to use the Fisher information matrix (FIM), which quantifies the expected information a particular experiment will reveal about model parameters. The finite state projection-based FIM (FSP-FIM) was recently developed to compute the FIM for discrete stochastic gene regulatory systems, whose complex response distributions do not satisfy standard assumptions of Gaussian variations. In this work, we develop the FSP-FIM analysis for a stochastic model of stress response genes in S. cerevisiae under time-varying MAPK induction. We verify this FSP-FIM analysis and use it to optimize the number of cells that should be quantified at particular times to learn as much as possible about the model parameters. We then extend the FSP-FIM approach to explore how different measurement times or genetic modifications help to minimize uncertainty in the sensing of extracellular environments, and we experimentally validate the FSP-FIM to rank single-cell experiments for their abilities to minimize estimation uncertainty of NaCl concentrations during yeast osmotic shock. This work demonstrates the potential of quantitative models to not only make sense of modern biological datasets but to close the loop between quantitative modeling and experimental data collection.
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Viviescas, Álvaro, Gustavo Chio Cho, Oscar Begambre, Wilson Hernandez, and Carlos Alberto Riveros-Jerez. "Optimal Sensor Placement of a Box Girder Bridge Using Mode Shapes Obtained from Numerical Analysis and Field Testing." Revista EIA 17, no. 34 (October 12, 2020): 1–12. http://dx.doi.org/10.24050/reia.v17i34.1296.

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This paper presents a comparative study of an Optimal Sensor Placement (OSP) implementation conducted in a box girder bridge using experimental and numerical mode shapes obtained at different construction stages. It is widely recognized that monitoring the dynamic response of bridges during different construction stages provides valuable information to adjust design considerations. Therefore, there is a need for the development of OSP implementations in order to find the optimal number of sensors needed for real applications. In the present study, an OPS method based on the maximization of the Fisher Information Matrix (FIM) is used. The use of experimentally derived and numerical based mode shapes is considered in the determination of the optimal sensor locations. Field testing results previously conducted before connecting the central segment of the main span are also included in this study. The asphalt pavement weight effect in OSP determination is also analyzed by considering field testing.
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Dissertations / Theses on the topic "Fisher information matrix (FIM)"

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Roy, Prateep Kumar. "Analysis & design of control for distributed embedded systems under communication constraints." Phd thesis, Université Paris-Est, 2009. http://tel.archives-ouvertes.fr/tel-00534012.

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Les Systèmes de Contrôle Embarqués Distribués (SCED) utilisent les réseaux de communication dans les boucles de rétroaction. Étant donné que les systèmes SCED ont une puissance de batterie, une bande passante de communication et une puissance de calcul limitée, les débits des données ou des informations transmises sont bornées et ils peuvent affecter leur stabilité. Ceci nous amène à élargir le spectre de notre étude et y intégrer une étude sur la relation entre la théorie du contrôle d'un coté et celle de l'information de l'autre. La contrainte de débit de données induit la quantification des signaux tandis que les aspects de calcul temps réel et de communication induit des événements asynchrones qui ne sont plus réguliers ou périodiques. Ces deux phénomènes donnent au SCED une double nature, continue et discrète, et en font des cas d'étude spécifiques. Dans cette thèse, nous analysons la stabilité et la performance de SCED du point de vue de la théorie de l'information et du contrôle. Pour les systèmes linéaires, nous montrons l'importance du compromis entre la quantité d'information communiquée et les objectifs de contrôle, telles que la stabilité, la contrôlabilité/observabilité et les performances. Une approche de conception conjointe de contrôle et de communication (en termes de débit d'information au sens de Shannon) des SCED est étudiée. Les principaux résultats de ces travaux sont les suivants : nous avons prouvé que la réduction d'entropie (ce qui correspond à la réduction d'incertitude) dépend du Grammien de contrôlabilité. Cette réduction est également liée à l'information mutuelle de Shannon. Nous avons démontré que le Grammien de contrôlabilité constitue une métrique de l'entropie théorique de l'information en ce qui concerne les bruits induits par la quantification. La réduction de l'influence de ces bruits est équivalente à la réduction de la norme du Grammien de contrôlabilité. Nous avons établi une nouvelle relation entre la matrice d'information de Fisher (FIM) et le Grammien de Contrôlabilité (CG) basé sur la théorie de l'estimation et la théorie de l'information. Nous proposons un algorithme qui distribue de manière optimale les capacités de communication du réseau entre un nombre "n" d'actionneurs et/ou systèmes concurrents se basant sur la réduction de la norme du Grammien de Contrôlabilité
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Roy, Prateep Kumar. "Analyse et conception de la commande des systèmes embarqués distribués sous des contraintes de communication." Phd thesis, Université Paris-Est, 2009. http://tel.archives-ouvertes.fr/tel-00532883.

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Les Systèmes de Contrôle Embarqués Distribués (SCED) utilisent les réseaux de communication dans les boucles de rétroaction. Étant donné que les systèmes SCED ont une puissance de batterie, une bande passante de communication et une puissance de calcul limitée, les débits des données ou des informations transmises sont bornées et ils peuvent affecter leur stabilité. Ceci nous amène à élargir le spectre de notre étude et y intégrer une étude sur la relation entre la théorie du contrôle d'un coté et celle de l'information de l'autre. La contrainte de débit de données induit la quantification des signaux tandis que les aspects de calcul temps réel et de communication induit des événements asynchrones qui ne sont plus réguliers ou périodiques. Ces deux phénomènes donnent au SCED une double nature, continue et discrète, et en font des cas d'étude spécifiques. Dans cette thèse, nous analysons la stabilité et la performance de SCED du point de vue de la théorie de l'information et du contrôle. Pour les systèmes linéaires, nous montrons l'importance du compromis entre la quantité d'information communiquée et les objectifs de contrôle, telles que la stabilité, la contrôlabilité/observabilité et les performances. Une approche de conception conjointe de contrôle et de communication (en termes de débit d'information au sens de Shannon) des SCED est étudiée. Les principaux résultats de ces travaux sont les suivants : nous avons prouvé que la réduction d'entropie (ce qui correspond à la réduction d'incertitude) dépend du Grammien de contrôlabilité. Cette réduction est également liée à l'information mutuelle de Shannon. Nous avons démontré que le Grammien de contrôlabilité constitue une métrique de l'entropie théorique de l'information en ce qui concerne les bruits induits par la quantification. La réduction de l'influence de ces bruits est équivalente à la réduction de la norme du Grammien de contrôlabilité. Nous avons établi une nouvelle relation entre la matrice d'information de Fisher (FIM) et le Grammien de Contrôlabilité (CG) basé sur la théorie de l'estimation et la théorie de l'information. Nous proposons un algorithme qui distribue de manière optimale les capacités de communication du réseau entre un nombre "n" d'actionneurs et/ou systèmes concurrents se basant sur la réduction de la norme du Grammien de Contrôlabilité
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Pazman, Andrej. "Correlated optimum design with parametrized covariance function. Justification of the Fisher information matrix and of the method of virtual noise." Institut für Statistik und Mathematik, WU Vienna University of Economics and Business, 2004. http://epub.wu.ac.at/562/1/document.pdf.

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We consider observations of a random field (or a random process), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. In the first part we show that under the assumption that the errors are normal with small variances, even when the number of observations is small, the ML estimators of both parameters are approximately unbiased, uncorrelated, with variances given by the inverse of the Fisher information matrix. In the second part we are extending the result of Pazman & Müller (2001) to the case of parametrized covariance function, namely we prove that the optimum designs with and without the presence of the virtual noise are identical. This in principle justify the use the method of virtual noise as a computational device also in this case. (authors' abstract)
Series: Research Report Series / Department of Statistics and Mathematics
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Strömberg, Eric. "Faster Optimal Design Calculations for Practical Applications." Thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-150802.

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PopED is a software developed by the Pharmacometrics Research Group at the Department of Pharmaceutical Biosiences, Uppsala University written mainly in MATLAB. It uses pharmacometric population models to describe the pharmacokinetics and pharmacodynamics of a drug and then estimates an optimal design of a trial for that drug. With optimization calculations in average taking a very long time, it was desirable to increase the calculation speed of the software by parallelizing the serial calculation script. The goal of this project was to investigate different methods of parallelization and implement the method which seemed the best for the circumstances.The parallelization was implemented in C/C++ by using Open MPI and tested on the UPPMAX Kalkyl High-Performance Computation Cluster. Some alterations were made in the original MATLAB script to adapt PopED to the new parallel code. The methods which where parallelized included the Random Search and the Line Search algorithms. The testing showed a significant performance increase, with effectiveness per active core rangingfrom 55% to 89% depending on model and number of evaluated designs.
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Panas, Dagmara. "Model-based analysis of stability in networks of neurons." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28883.

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Neurons, the building blocks of the brain, are an astonishingly capable type of cell. Collectively they can store, manipulate and retrieve biologically important information, allowing animals to learn and adapt to environmental changes. This universal adaptability is widely believed to be due to plasticity: the readiness of neurons to manipulate and adjust their intrinsic properties and strengths of connections to other cells. It is through such modifications that associations between neurons can be made, giving rise to memory representations; for example, linking a neuron responding to the smell of pancakes with neurons encoding sweet taste and general gustatory pleasure. However, this malleability inherent to neuronal cells poses a dilemma from the point of view of stability: how is the brain able to maintain stable operation while in the state of constant flux? First of all, won’t there occur purely technical problems akin to short-circuiting or runaway activity? And second of all, if the neurons are so easily plastic and changeable, how can they provide a reliable description of the environment? Of course, evidence abounds to testify to the robustness of brains, both from everyday experience and scientific experiments. How does this robustness come about? Firstly, many control feedback mechanisms are in place to ensure that neurons do not enter wild regimes of behaviour. These mechanisms are collectively known as homeostatic plasticity, since they ensure functional homeostasis through plastic changes. One well-known example is synaptic scaling, a type of plasticity ensuring that a single neuron does not get overexcited by its inputs: whenever learning occurs and connections between cells get strengthened, subsequently all the neurons’ inputs get downscaled to maintain a stable level of net incoming signals. And secondly, as hinted by other researchers and directly explored in this work, networks of neurons exhibit a property present in many complex systems called sloppiness. That is, they produce very similar behaviour under a wide range of parameters. This principle appears to operate on many scales and is highly useful (perhaps even unavoidable), as it permits for variation between individuals and for robustness to mutations and developmental perturbations: since there are many combinations of parameters resulting in similar operational behaviour, a disturbance of a single, or even several, parameters does not need to lead to dysfunction. It is also that same property that permits networks of neurons to flexibly reorganize and learn without becoming unstable. As an illustrative example, consider encountering maple syrup for the first time and associating it with pancakes; thanks to sloppiness, this new link can be added without causing the network to fire excessively. As has been found in previous experimental studies, consistent multi-neuron activity patterns arise across organisms, despite the interindividual differences in firing profiles of single cells and precise values of connection strengths. Such activity patterns, as has been furthermore shown, can be maintained despite pharmacological perturbation, as neurons compensate for the perturbed parameters by adjusting others; however, not all pharmacological perturbations can be thus amended. In the present work, it is for the first time directly demonstrated that groups of neurons are by rule sloppy; their collective parameter space is mapped to reveal which are the sensitive and insensitive parameter combinations; and it is shown that the majority of spontaneous fluctuations over time primarily affect the insensitive parameters. In order to demonstrate the above, hippocampal neurons of the rat were grown in culture over multi-electrode arrays and recorded from for several days. Subsequently, statistical models were fit to the activity patterns of groups of neurons to obtain a mathematically tractable description of their collective behaviour at each time point. These models provide robust fits to the data and allow for a principled sensitivity analysis with the use of information-theoretic tools. This analysis has revealed that groups of neurons tend to be governed by a few leader units. Furthermore, it appears that it was the stability of these key neurons and their connections that ensured the stability of collective firing patterns across time. The remaining units, in turn, were free to undergo plastic changes without risking destabilizing the collective behaviour. Together with what has been observed by other researchers, the findings of the present work suggest that the impressively adaptable yet robust functioning of the brain is made possible by the interplay of feedback control of few crucial properties of neurons and the general sloppy design of networks. It has, in fact, been hypothesised that any complex system subject to evolution is bound to rely on such design: in order to cope with natural selection under changing environmental circumstances, it would be difficult for a system to rely on tightly controlled parameters. It might be, therefore, that all life is just, by nature, sloppy.
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Perez-Ramirez, Javier. "An Opportunistic Relaying Scheme for Optimal Communications and Source Localization." International Foundation for Telemetering, 2012. http://hdl.handle.net/10150/581448.

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ITC/USA 2012 Conference Proceedings / The Forty-Eighth Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2012 / Town and Country Resort & Convention Center, San Diego, California
The selection of relay nodes (RNs) for optimal communication and source location estimation is studied. The RNs are randomly placed at fixed and known locations over a geographical area. A mobile source senses and collects data at various locations over the area and transmits the data to a destination node with the help of the RNs. The destination node not only needs to collect the sensed data but also the location of the source where the data is collected. Hence, both high quality data collection and the correct location of the source are needed. Using the measured distances between the relays and the source, the destination estimates the location of the source. The selected RNs must be optimal for joint communication and source location estimation. We show in this paper how this joint optimization can be achieved. For practical decentralized selection, an opportunistic RN selection algorithm is used. Bit error rate performance as well as mean squared error in location estimation are presented and compared to the optimal relay selection results.
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Perez-Ramirez, Javier. "Relay Selection for Multiple Source Communications and Localization." International Foundation for Telemetering, 2013. http://hdl.handle.net/10150/579585.

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ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV
Relay selection for optimal communication as well as multiple source localization is studied. We consider the use of dual-role nodes that can work both as relays and also as anchors. The dual-role nodes and multiple sources are placed at fixed locations in a two-dimensional space. Each dual-role node estimates its distance to all the sources within its radius of action. Dual-role selection is then obtained considering all the measured distances and the total SNR of all sources-to-destination channels for optimal communication and multiple source localization. Bit error rate performance as well as mean squared error of the proposed optimal dual-role node selection scheme are presented.
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Maltauro, Tamara Cantú. "Algoritmo genético aplicado à determinação da melhor configuração e do menor tamanho amostral na análise da variabilidade espacial de atributos químicos do solo." Universidade Estadual do Oeste do Paraná, 2018. http://tede.unioeste.br/handle/tede/3920.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
It is essential to determine a sampling design with a size that minimizes operating costs and maximizes the results quality throughout a trial setting that involves the study of spatial variability of chemical attributes on soil. Thus, this trial aimed at resizing a sample configuration with the least possible number of points for a commercial area composed of 102 points, regarding the information on spatial variability of soil chemical attributes to optimize the process. Initially, Monte Carlo simulations were carried out, assuming Gaussian, isotropic, and exponential model for semi-variance function and three initial sampling configurations: systematic, simple random and lattice plus close pairs. The Genetic Algorithm (GA) was used to obtain simulated data and chemical attributes of soil, in order to resize the optimized sample, considering two objective-functions. They are based on the efficiency of spatial prediction and geostatistical model estimation, which are respectively: maximization of global accuracy precision and minimization of functions based on Fisher information matrix. It was observed by the simulated data that for both objective functions, when the nugget effect and range varied, samplings usually showed the lowest values of objectivefunction, whose nugget effect was 0 and practical range was 0.9. And the increase in practical range has generated a slight reduction in the number of optimized sampling points for most cases. In relation to the soil chemical attributes, GA was efficient in reducing the sample size with both objective functions. Thus, sample size varied from 30 to 35 points in order to maximize global accuracy precision, which corresponded to 29.41% to 34.31% of the initial mesh, with a minimum spatial prediction similarity to the original configuration, equal to or greater than 85%. It is noteworthy that such data have reflected on the optimization process, which have similarity between the maps constructed with sample configurations: original and optimized. Nevertheless, the sample size of the optimized sample varied from 30 to 40 points to minimize the function based on Fisher information matrix, which corresponds to 29.41% and 39.22% of the original mesh, respectively. However, there was no similarity between the constructed maps when considering the initial and optimum sample configuration. For both objective functions, the soil chemical attributes showed mild spatial dependence for the original sample configuration. And, most of the attributes showed mild or strong spatial dependence for optimum sample configuration. Thus, the optimization process was efficient when applied to both simulated data and soil chemical attributes.
É necessário determinar um esquema de amostragem com um tamanho que minimize os custos operacionais e maximize a qualidade dos resultados durante a montagem de um experimento que envolva o estudo da variabilidade espacial de atributos químicos do solo. Assim, o objetivo deste trabalho foi redimensionar uma configuração amostral com o menor número de pontos possíveis para uma área comercial composta por 102 pontos, considerando a informação sobre a variabilidade espacial de atributos químicos do solo no processo de otimização. Inicialmente, realizaram-se simulações de Monte Carlo, assumindo as variáveis estacionárias Gaussiana, isotrópicas, modelo exponencial para a função semivariância e três configurações amostrais iniciais: sistemática, aleatória simples e lattice plus close pairs. O Algoritmo Genético (AG) foi utilizado para a obtenção dos dados simulados e dos atributos químicos do solo, a fim de se redimensionar a amostra otimizada, considerando duas funções-objetivo. Essas estão baseadas na eficiência quanto à predição espacial e à estimação do modelo geoestatístico, as quais são respectivamente: a maximização da medida de acurácia exatidão global e a minimização de funções baseadas na matriz de informação de Fisher. Observou-se pelos dados simulados que, para ambas as funções-objetivo, quando o efeito pepita e o alcance variaram, em geral, as amostragens apresentaram os menores valores da função-objetivo, com efeito pepita igual a 0 e alcance prático igual a 0,9. O aumento do alcance prático gerou uma leve redução do número de pontos amostrais otimizados para a maioria dos casos. Em relação aos atributos químicos do solo, o AG, com ambas as funções-objetivo, foi eficiente quanto à redução do tamanho amostral. Para a maximização da exatidão global, tem-se que o tamanho amostral da nova amostra reduzida variou entre 30 e 35 pontos que corresponde respectivamente a 29,41% e a 34,31% da malha inicial, com uma similaridade mínima de predição espacial, em relação à configuração original, igual ou superior a 85%. Vale ressaltar que tais dados refletem no processo de otimização, os quais apresentam similaridade entres os mapas construídos com as configurações amostrais: original e otimizada. Todavia, o tamanho amostral da amostra otimizada variou entre 30 e 40 pontos para minimizar a função baseada na matriz de informaçãode Fisher, a qual corresponde respectivamente a 29,41% e 39,22% da malha original. Mas, não houve similaridade entre os mapas elaborados quando se considerou a configuração amostral inicial e a otimizada. Para ambas as funções-objetivo, os atributos químicos do solo apresentaram moderada dependência espacial para a configuração amostral original. E, a maioria dos atributos apresentaram moderada ou forte dependência espacial para a configuração amostral otimizada. Assim, o processo de otimização foi eficiente quando aplicados tanto nos dados simulados como nos atributos químicos do solo.
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9

Achanta, Hema Kumari. "Optimal sensing matrices." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1421.

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Location information is of extreme importance in every walk of life ranging from commercial applications such as location based advertising and location aware next generation communication networks such as the 5G networks to security based applications like threat localization and E-911 calling. In indoor and dense urban environments plagued by multipath effects there is usually a Non Line of Sight (NLOS) scenario preventing GPS based localization. Wireless localization using sensor networks provides a cost effective and accurate solution to the wireless source localization problem. Certain sensor geometries show significantly poor performance even in low noise scenarios when triangulation based localization methods are used. This brings the need for the design of an optimum sensor placement scheme for better performance in the source localization process. The optimum sensor placement is the one that optimizes the underlying Fisher Information Matrix(FIM) . This thesis will present a class of canonical optimum sensor placements that produce the optimum FIM for N-dimensional source localization N greater than or equal to 2 for a case where the source location has a radially symmetric probability density function within a N-dimensional sphere and the sensors are all on or outside the surface of a concentric outer N-dimensional sphere. While the canonical solution that we designed for the 2D problem represents optimum spherical codes, the study of 3 or higher dimensional design provides great insights into the design of measurement matrices with equal norm columns that have the smallest possible condition number. Such matrices are of importance in compressed sensing based applications. This thesis also presents an optimum sensing matrix design for energy efficient source localization in 2D. Specifically, the results relate to the worst case scenario when the minimum number of sensors are active in the sensor network. We also propose a distributed control law that guides the motion of the sensors on the circumference of the outer circle so that achieve the optimum sensor placement with minimum communication overhead. The design of equal norm column sensing matrices has a variety of other applications apart from the optimum sensor placement for N-dimensional source localization. One such application is fourier analysis in Magnetic Resonance Imaging (MRI). Depending on the method used to acquire the MR image, one can choose an appropriate transform domain that transforms the MR image into a sparse image that is compressible. Some such transform domains include Wavelet Transform and Fourier Transform. The inherent sparsity of the MR images in an appropriately chosen transform domain, motivates one of the objectives of this thesis which is to provide a method for designing a compressive sensing measurement matrix by choosing a subset of rows from the Discrete Fourier Transform (DFT) matrix. This thesis uses the spark of the matrix as the design criterion. The spark of a matrix is defined as the smallest number of linearly dependent columns of the matrix. The objective is to select a subset of rows from the DFT matrix in order to achieve maximum spark. The design procedure leads us to an interest study of coprime conditions on the row indices chosen with the size of the DFT matrix.
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Bastian, Michael R. "Neural Networks and the Natural Gradient." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/539.

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Neural network training algorithms have always suffered from the problem of local minima. The advent of natural gradient algorithms promised to overcome this shortcoming by finding better local minima. However, they require additional training parameters and computational overhead. By using a new formulation for the natural gradient, an algorithm is described that uses less memory and processing time than previous algorithms with comparable performance.
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Books on the topic "Fisher information matrix (FIM)"

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Song, Zhen. Optimal Observation for Cyber-physical Systems: A Fisher-information-matrix-based Approach. London: Springer London, 2009.

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Chen, YangQuan, Zhen Song, Chellury R. Sastry, and Nazif C. Tas. Optimal Observation for Cyber-physical Systems: A Fisher-information-matrix-based Approach. Springer, 2014.

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Cheng, Russell. The Skew Normal Distribution. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0012.

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This chapter considers the univariate skew-normal distribution, a generalization of the normal that includes the normal as a special case. The most natural parametrization is non-standard. This is because the Fisher information matrix is then singular at the true parameter value when the true model is the normal special case. The log-likelihood is then particularly flat in a certain coordinate direction. Standard theory cannot then be used to calculate the asymptotic distribution of all the parameter estimates. This problem can be handled using an alternative parametrization. There is another special case: the half/folded normal distribution. This occurs in the usual parametrization when the shape parameter is infinite. This is not a problem computationally and is easily handled. There are many generalizations to skew-t distributions and to tractable multivariate forms and regression versions. A very brief review is included of these.
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Book chapters on the topic "Fisher information matrix (FIM)"

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Zhang, C. Y., H. X. Chen, M. S. Chen, and Z. H. Sun. "Image Matrix Fisher Discriminant Analysis (IMFDA)- 2D Matrix Based Face Image Retrieval Algorithm." In Advances in Web-Age Information Management, 894–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11563952_99.

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Sakano, Hitoshi, Tsukasa Ohashi, Akisato Kimura, Hiroshi Sawada, and Katsuhiko Ishiguro. "Extended Fisher Criterion Based on Auto-correlation Matrix Information." In Lecture Notes in Computer Science, 409–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34166-3_45.

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Kawai, R. "On Singularity of Fisher Information Matrix for Stochastic Processes Under High Frequency Sampling." In Numerical Mathematics and Advanced Applications 2011, 841–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33134-3_87.

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Furusho, Yasutaka, and Kazushi Ikeda. "Effects of Skip-Connection in ResNet and Batch-Normalization on Fisher Information Matrix." In Proceedings of the International Neural Networks Society, 341–48. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16841-4_35.

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Bozdogan, Hamparsum. "Choosing the Number of Component Clusters in the Mixture-Model Using a New Informational Complexity Criterion of the Inverse-Fisher Information Matrix." In Information and Classification, 40–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-50974-2_5.

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Leonov, Sergei, and Alexander Aliev. "Approximation of the Fisher Information Matrix for Nonlinear Mixed Effects Models in Population PK/PD Studies." In Contributions to Statistics, 145–52. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00218-7_17.

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Poston, Wendy L., Carey E. Priebe, and O. Thomas Holland. "Maximizing the Fisher Information Matrix in Discrete-Time Systems." In Control and Dynamic Systems, 131–55. Elsevier, 1995. http://dx.doi.org/10.1016/s0090-5267(06)80017-4.

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"Multi-Sensor Management: Multi-Sensor Scheduling for Target Tracking Using Fisher Information Matrix Perturbation." In International Conference on Information Technology and Computer Science, 3rd (ITCS 2011), 174–77. ASME Press, 2011. http://dx.doi.org/10.1115/1.859742.paper43.

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Conference papers on the topic "Fisher information matrix (FIM)"

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Costa, S. I. R., S. A. Santos, and J. E. Strapasson. "Fisher information matrix and hyperbolic geometry." In IEEE Information Theory Workshop, 2005. IEEE, 2005. http://dx.doi.org/10.1109/itw.2005.1531851.

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ALLAHDADIAN, SAEID, MICHAEL DÖHLER, CARLOS VENTURA, and LAURENT MEVEL. "Hierarchical Fisher-information-matrix-based Clustering." In Structural Health Monitoring 2019. Lancaster, PA: DEStech Publications, Inc., 2019. http://dx.doi.org/10.12783/shm2019/32478.

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Wang, Zhan, and Gamini Dissanayake. "Observability analysis of SLAM using fisher information matrix." In 2008 10th International Conference on Control, Automation, Robotics and Vision (ICARCV). IEEE, 2008. http://dx.doi.org/10.1109/icarcv.2008.4795699.

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Agarwal, A. "Large N Matrix Models and Noncommutative Fisher Information." In THEORETICAL PHYSICS: MRST 2002: A Tribute to George Leibbrandt. AIP, 2002. http://dx.doi.org/10.1063/1.1524569.

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Das, Sonjoy, James C. Spall, and Roger Ghanem. "Efficient Monte Carlo computation of Fisher information matrix using prior information." In the 2007 Workshop. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1660877.1660912.

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Lei, Ming, Christophe Baehr, and Pierre Del Moral. "Fisher information matrix-based nonlinear system conversion for state estimation." In 2010 8th IEEE International Conference on Control and Automation (ICCA). IEEE, 2010. http://dx.doi.org/10.1109/icca.2010.5524066.

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Mishra, Vinod K. "Quantum fisher information matrix of a single qutrit in lambda configuration." In Quantum Information Science, Sensing, and Computation XIII, edited by Michael Hayduk and Eric Donkor. SPIE, 2021. http://dx.doi.org/10.1117/12.2587973.

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Meng, Lingyao, and James C. Spall. "Efficient computation of the Fisher information matrix in the EM algorithm." In 2017 51st Annual Conference on Information Sciences and Systems (CISS). IEEE, 2017. http://dx.doi.org/10.1109/ciss.2017.7926126.

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Spall, James C. "Improved methods for Monte Carlo estimation of the fisher information matrix." In 2008 American Control Conference (ACC '08). IEEE, 2008. http://dx.doi.org/10.1109/acc.2008.4586850.

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Sanayei, Masoud, and Chitra N. Javdekar. "Sensor Placement for Parameter Estimation of Structures Using Fisher Information Matrix." In Seventh International Conference on Applications of Advanced Technologies in Transportation (AATT). Reston, VA: American Society of Civil Engineers, 2002. http://dx.doi.org/10.1061/40632(245)49.

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Reports on the topic "Fisher information matrix (FIM)"

1

Ortiz, M. Analytical Methods of Approximating the Fisher Information Matrix for the Lognormal Distribution. Office of Scientific and Technical Information (OSTI), August 2018. http://dx.doi.org/10.2172/1557955.

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