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

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

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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7

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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8

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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10

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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11

Petersen, B., K. Gernaey, and P. A. Vanrolleghem. "Practical identifiability of model parameters by combined respirometric-titrimetric measurements." Water Science and Technology 43, no. 7 (April 1, 2001): 347–55. http://dx.doi.org/10.2166/wst.2001.0444.

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An earlier study on theoretical identifiability of parameters for a two-step nitrification model showed that a unique estimation of the yield YA1 is possible with combined respirometric-titrimetric data, contrary to the case where only one type of measurement is available. Here, the practical identifiability of model parameters was investigated via evaluation of the output sensitivity functions and the corresponding Fisher Information Matrix (FIM). It appeared that the FIM was not sufficiently powerful to predict the practical identifiability of this case with combined measurements as parameters could indeed be identified despite the fact that the FIM became singular. The accuracy of parameter estimates based on respirometric and titrimetric data and combination thereof was also investigated. Estimation on titrimetric data (Hp) was very accurate and a fast convergence of the objective function towards a minimum was obtained. The latter also holds for estimation on oxygen uptake rate data (rO), however with a lower accuracy. Parameter estimation based on oxygen concentration data (SO) was more complex but resulted in a higher accuracy. Thus, when the highest accuracy is needed it is recommended to estimate parameters initially on Hp and/or rO data, and to subsequently use these parameters as initial values for final, and more accurate estimation on SO data.

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12

Wang, Dongzhen, Daqing Huang, Cheng Xu, and Wei Han. "A Closed-Form Method for Simultaneous Target Localization and UAV Trajectory Optimization." Applied Sciences 11, no. 1 (December 24, 2020): 114. http://dx.doi.org/10.3390/app11010114.

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Unmanned aerial vehicles (UAVs) play a key role in modern surveillance-related missions. A major task for performing these missions is to find the precise location of a moving target in real-time, for which the main challenge is to estimate the target position to high precision using the noisy measurements from the airborne sensors. In this paper, we present a closed-form on-line simultaneous target localization and UAV trajectory optimization method based on the visual platform, which can effectively minimize the localization uncertainty to the target. The proposed method can be elucidated explicitly using two phases, of which, in the target localization phase, the expended information filtering (EIF) is exploited, which can express the predicted Fisher information matrix (FIM) of the target explicitly and iteratively, and in the UAV trajectory optimization phase, the property of the predicted FIM is exploited to establish the UAV waypoint optimization objective by taking account of the UAV motion limit. Compared with existing methods of the same class, the proposed method not only estimates the next target position more correctly, but also takes the error of the target motion into consideration, thus improving the effectiveness of the optimized UAV trajectory. Both simulations and field experiments were conducted, which show that the proposed method outperformed the existing methods.

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13

Duarte, Belmiro P. M., Anthony C. Atkinson, José F. O. Granjo, and Nuno M. C. Oliveira. "Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming." Processes 7, no. 11 (November 8, 2019): 834. http://dx.doi.org/10.3390/pr7110834.

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Liquid–liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three optimality criteria (D-, A- and E-optimal) are exemplified. The approach is demonstrated for two ternary systems where different sets of parameters are to be estimated.

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Hou, Zhaozheng. "Introducing Parameter Clustering to the OED Procedure for Model Calibration of a Synthetic Inducible Promoter in S. cerevisiae." Processes 9, no. 6 (June 16, 2021): 1053. http://dx.doi.org/10.3390/pr9061053.

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In recent years, synthetic gene circuits for adding new cell features have become one of the most powerful tools in biological and pharmaceutical research and development. However, because of the inherent non-linearity and noisy experimental data, the experiment-based model calibration of these synthetic parts is perceived as a laborious and time-consuming procedure. Although the optimal experimental design (OED) based on the Fisher information matrix (FIM) has been proved to be an effective means to improve the calibration efficiency, the required calculation increases dramatically with the model size (parameter number). To reduce the OED complexity without losing the calibration accuracy, this paper proposes two OED approaches with different parameter clustering methods and validates the accuracy of calibrated models with in-silico experiments. A model of an inducible synthetic promoter in S. cerevisiae is adopted for bench-marking. The comparison with the traditional off-line OED approach suggests that the OED approaches with both of the clustering methods significantly reduce the complexity of OED problems (for at least 49.0%), while slightly improving the calibration accuracy (11.8% and 19.6% lower estimation error in average for FIM-based and sensitivity-based approaches). This study implicates that for calibrating non-linear models of biological pathways, cluster-based OED could be a beneficial approach to improve the efficiency of optimal experimental design.

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Li, Zhenliang, Peili Lu, Daijun Zhang, and Tian Zhang. "Practical Identifiability Analysis and Optimal Experimental Design for the Parameter Estimation of the ASM2d-Based EBPR Anaerobic Submodel." Mathematical Problems in Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/9201085.

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Identifiability analysis is a precondition for reliable parameter estimation. Building on previous work on structural identifiability, this paper focuses on the practical identifiability and optimal experimental design (OED) of the EBPR anaerobic submodel. The nonnegative determinant of the Fisher information matrix (FIM) found in this study clearly demonstrates that the parametersYPO4,KA,qPHA, andXPAOin the submodel are practically identifiable usingSAandSPO4as the measured variables and fixingKPPas the default value. Furthermore, fixingKPPto study the practical identifiability of the other parameters and to estimate their values is shown to be valid. Subsequently, a modeling-based procedure for the OED for parameter estimation was proposed and applied successfully to anaerobic phosphorus release experiments. According to the FIMD-criterion, the optimal experimental condition was determined to be an initialSAconcentration of 300 mg/L. Under the optimal experimental condition, errors in the values ofYPO4,KA,qPHA, andXPAOare all below 20%, and the estimated values were 0.35 ± 0.02 mg P/mg COD, 3.88 ± 0.41 mg COD/L, 3.35 ± 0.27 mg P/(mgCOD⁎d-1), and 1500 ± 72 mg COD/L, respectively. Compared to the results from the nonoptimal experimental condition, the practical identifiability and the estimation precision of the four parameters were improved.

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Bo, Xu, Asghar Razzaqi, and Xiaoyu Wang. "Optimal Sensor Formation for 3D Cooperative Localization of AUVs Using Time Difference of Arrival (TDOA) Method." Sensors 18, no. 12 (December 15, 2018): 4442. http://dx.doi.org/10.3390/s18124442.

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The cooperative localization of submerged autonomous underwater vehicles (AUVs) using the Time Difference of Arrival (TDOA) measurements of surface AUV sensors is an effective method for many applications of AUVs. Proper positioning of the sensors to maximize the observability of the AUVs is very critical for cooperative localization. In this paper, a novel method for obtaining the optimal formation of sensor AUVs has been presented for the three-dimensional (3D) cooperative localization of targets using the TDOA technique. An evaluation function for estimating the optimal formation has been derived based on Fisher Information Matrix (FIM) theory for a single target as well as multiple-target cooperative localization systems. An iterative stepping algorithm has been followed to solve the evaluation function and obtain the optimal positions of the sensors. The algorithm ensured that the computation complexity should remain limited, even when the number of sensor AUVs is increased. Various simulation examples are then presented to calculate the optimal formation for different systems/situations. The effect of the position of the reference sensor and operating depth of the target AUVs on the optimal formation of the sensors has also been studied, and conclusions are drawn. For implementation of the proposed method for more practical scenarios, a simulation example is also presented for cases when the target’s position is only known with uncertainty.

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17

Chen, Yu, and Haidong Yuan. "Maximal quantum Fisher information matrix." New Journal of Physics 19, no. 6 (June 23, 2017): 063023. http://dx.doi.org/10.1088/1367-2630/aa723d.

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18

Ludwig, Monika. "Fisher information and matrix-valued valuations." Advances in Mathematics 226, no. 3 (February 2011): 2700–2711. http://dx.doi.org/10.1016/j.aim.2010.08.021.

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19

Kowalski, Andres M., and Angelo Plastino. "Decoherence, Anti-Decoherence, and Fisher Information." Entropy 23, no. 8 (August 12, 2021): 1035. http://dx.doi.org/10.3390/e23081035.

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In this work, we study quantum decoherence as reflected by the dynamics of a system that accounts for the interaction between matter and a given field. The process is described by an important information geometry tool: Fisher’s information measure (FIM). We find that it appropriately describes this concept, detecting salient details of the quantum–classical changeover (qcc). A good description of the qcc report can thus be obtained; in particular, a clear insight into the role that the uncertainty principle (UP) plays in the pertinent proceedings is presented. Plotting FIM versus a system’s motion invariant related to the UP, one can also visualize how anti-decoherence takes place, as opposed to the decoherence process studied in dozens of papers. In Fisher terms, the qcc can be seen as an order (quantum)–disorder (classical, including chaos) transition.

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Hung, H. S., and M. Kaveh. "Fisher information matrix of the coherently averaged covariance matrix." IEEE Transactions on Signal Processing 39, no. 6 (June 1991): 1433–35. http://dx.doi.org/10.1109/78.136553.

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Ober, Raimund J. "The Fisher information matrix for linear systems." Systems & Control Letters 47, no. 3 (October 2002): 221–26. http://dx.doi.org/10.1016/s0167-6911(02)00190-1.

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Liu, Jing, Haidong Yuan, Xiao-Ming Lu, and Xiaoguang Wang. "Quantum Fisher information matrix and multiparameter estimation." Journal of Physics A: Mathematical and Theoretical 53, no. 2 (December 18, 2019): 023001. http://dx.doi.org/10.1088/1751-8121/ab5d4d.

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Gao, Xu, Daniel Gillen, and Hernando Ombao. "Fisher information matrix of binary time series." METRON 76, no. 3 (November 21, 2018): 287–304. http://dx.doi.org/10.1007/s40300-018-0145-3.

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Lee, Eun-Taik, and Hee-Chang Eun. "Optimal sensor placements using modified Fisher information matrix and effective information algorithm." International Journal of Distributed Sensor Networks 17, no. 6 (June 2021): 155014772110230. http://dx.doi.org/10.1177/15501477211023022.

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This article presents an optimal sensor placement algorithm for modifying the Fisher information matrix and effective information. The modified Fisher information matrix and effective information are expressed using a dynamic equation constrained by the condensed relationship of the incomplete mode shape matrix. The mode shape matrix row corresponding to the master degree of freedom of the lowest-contribution Fisher information matrix and effective information indices is moved to the slave degree of freedom during each iteration to obtain an updated shape matrix, which is then used in subsequent calculations. The iteration is repeated until the target sensors attain the targeted number of modes. The numerical simulations are then applied to compare the optimal sensor placement results obtained using the number of installed sensors, and the contribution matrices using the Fisher information matrix and effective information approaches are compared based on the proposed parameter matrix. The mode-shape-based optimal sensor placement approach selects the optimal sensor layout at the positions to uniformly allocate the entire degree of freedom. The numerical results reveal that the proposed F-based and effective information–based approaches lead to slightly different results, depending on the number of parameter matrix modes; however, the resulting final optimal sensor placement is included in a group of common candidate sensor locations. However, the resulting final optimal sensor placement is included in a group of common candidate sensor locations.

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Brazauskas, Vytaras. "Fisher information matrix for the Feller–Pareto distribution." Statistics & Probability Letters 59, no. 2 (September 2002): 159–67. http://dx.doi.org/10.1016/s0167-7152(02)00143-8.

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Paul, Sudhir R., Uditha Balasooriya, and Tathagata Banerjee. "Fisher Information Matrix of the Dirichlet-multinomial Distribution." Biometrical Journal 47, no. 2 (April 2005): 230–36. http://dx.doi.org/10.1002/bimj.200410103.

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Jauffret, Claude. "Observability and fisher information matrix in nonlinear regression." IEEE Transactions on Aerospace and Electronic Systems 43, no. 2 (April 2007): 756–59. http://dx.doi.org/10.1109/taes.2007.4285368.

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Kagan, Abram, and Paul J. Smith. "Multivariate normal distributions, Fisher information and matrix inequalities." International Journal of Mathematical Education in Science and Technology 32, no. 1 (January 2001): 91–96. http://dx.doi.org/10.1080/00207390121565.

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Kagan, Abram, and Paul J. Smith. "Multivariate normal distributions, Fisher information and matrix inequalities." International Journal of Mathematical Education 32, no. 1 (January 1, 2001): 91–96. http://dx.doi.org/10.1080/00207390150207086.

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Klein, André. "Matrix Algebraic Properties of the Fisher Information Matrix of Stationary Processes." Entropy 16, no. 4 (April 8, 2014): 2023–55. http://dx.doi.org/10.3390/e16042023.

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Boyom, Michel Nguiffo, and Robert A. Wolak. "Transversely Hessian foliations and information geometry." International Journal of Mathematics 27, no. 11 (October 2016): 1650092. http://dx.doi.org/10.1142/s0129167x16500920.

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A family of probability distributions parametrized by an open domain [Formula: see text] in [Formula: see text] defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry, the standard assumption has been that the Fisher information matrix tensor is positive definite defining in this way a Riemannian metric on [Formula: see text]. It seems to be quite a strong condition. In general, not much can be said about the Fisher information matrix tensor. To develop a more general theory, we weaken the assumption and replace “positive definite” by the existence of a suitable torsion-free connection. It permits us to define naturally a foliation with a transversely Hessian structure. We develop the theory of transversely Hessian foliations along the lines of the classical theory.

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Chen, Chong-Bin, and Fu-Wen Shu. "Towards a Fisher-Information Description of Complexity in de Sitter Universe." Universe 5, no. 12 (November 29, 2019): 221. http://dx.doi.org/10.3390/universe5120221.

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Recent developments on holography and quantum information physics suggest that quantum information theory has come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing quantum gravity effects. How to apply this idea to a realistic universe is still unknown. Here, we show that some concepts in quantum information theory have cosmological descriptions. Particularly, we show that the complexity of a tensor network can be regarded as a Fisher information measure (FIM) of a dS universe, followed by several observations: (i) the holographic entanglement entropy has a tensor-network description and admits a information-theoretical interpretation, (ii) on-shell action of dS spacetime has a same description of FIM, (iii) complexity/action(CA) duality holds for dS spacetime. Our result is also valid for f ( R ) gravity, whose FIM exhibits the same features of a recent proposed L n norm complexity.

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Das, Sonjoy, James C. Spall, and Roger Ghanem. "Efficient Monte Carlo computation of Fisher information matrix using prior information." Computational Statistics & Data Analysis 54, no. 2 (February 2010): 272–89. http://dx.doi.org/10.1016/j.csda.2009.09.018.

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Cavicchioli, Maddalena. "Asymptotic Fisher information matrix of Markov switching VARMA models." Journal of Multivariate Analysis 157 (May 2017): 124–35. http://dx.doi.org/10.1016/j.jmva.2017.03.004.

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35

Klein, André, and Peter Spreij. "Transformed statistical distance measures and the fisher information matrix." Linear Algebra and its Applications 437, no. 2 (July 2012): 692–712. http://dx.doi.org/10.1016/j.laa.2012.03.002.

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Klein, A., and G. Melard. "Computation of the Fisher information matrix for SISO models." IEEE Transactions on Signal Processing 42, no. 3 (March 1994): 684–88. http://dx.doi.org/10.1109/78.277866.

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Park, Jeong-Soo, and Tae Yoon Kim. "Fisher information matrix for a four-parameter kappa distribution." Statistics & Probability Letters 77, no. 13 (July 2007): 1459–66. http://dx.doi.org/10.1016/j.spl.2007.03.002.

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Vahid, Milad R., Bernard Hanzon, and Raimund J. Ober. "Fisher Information Matrix for Single Molecules with Stochastic Trajectories." SIAM Journal on Imaging Sciences 13, no. 1 (January 2020): 234–64. http://dx.doi.org/10.1137/19m1242562.

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Nagar, Daya K., Edwin Zarrazola, and Luz Estela Sanchez. "Entropies and Fisher information matrix for extended beta distribution." Applied Mathematical Sciences 9 (2015): 3983–94. http://dx.doi.org/10.12988/ams.2015.53257.

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Scott, William Andrew. "Maximum likelihood estimation using the empirical fisher information matrix." Journal of Statistical Computation and Simulation 72, no. 8 (January 2002): 599–611. http://dx.doi.org/10.1080/00949650213744.

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Mahmoud, Mahmoud Riad, and Amani Shaheen Abd El-Ghafour. "Fisher Information Matrix for the Generalized Feller-Pareto Distribution." Communications in Statistics - Theory and Methods 44, no. 20 (April 2015): 4396–407. http://dx.doi.org/10.1080/03610926.2013.841933.

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Shi, Daoji. "Multivariate extreme value distribution and its fisher information matrix." Acta Mathematicae Applicatae Sinica 11, no. 4 (October 1995): 421–28. http://dx.doi.org/10.1007/bf02007180.

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Salicrú, M., and I. J. Taneja. "Connections of generalized divergence measures with Fisher information matrix." Information Sciences 72, no. 3 (August 1993): 251–69. http://dx.doi.org/10.1016/0020-0255(93)90093-2.

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Slyusar, V. I. "Fisher information matrix for models of systems based on face-splitting matrix products." Cybernetics and Systems Analysis 35, no. 4 (July 1999): 636–43. http://dx.doi.org/10.1007/bf02835859.

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Ober, R. J., Qiyue Zou, and Zhiping Lin. "Calculation of the fisher information matrix for multidimensional data sets." IEEE Transactions on Signal Processing 51, no. 10 (October 2003): 2679–91. http://dx.doi.org/10.1109/tsp.2003.816880.

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Enbin Song, Yunmin Zhu, Jie Zhou, and Zhisheng You. "Minimum Variance in Biased Estimation With Singular Fisher Information Matrix." IEEE Transactions on Signal Processing 57, no. 1 (January 2009): 376–81. http://dx.doi.org/10.1109/tsp.2008.2005869.

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Besson, Olivier, and Yuri I. Abramovich. "On the Fisher Information Matrix for Multivariate Elliptically Contoured Distributions." IEEE Signal Processing Letters 20, no. 11 (November 2013): 1130–33. http://dx.doi.org/10.1109/lsp.2013.2281914.

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BENTARZI, MOHAMED, and ABDELHAKIM AKNOUCHE. "Calculation of the Fisher Information Matrix for Periodic ARMA Models." Communications in Statistics - Theory and Methods 34, no. 4 (April 2005): 891–903. http://dx.doi.org/10.1081/sta-200054428.

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Guo, Weili, Yew-Soon Ong, Yingjiang Zhou, Jaime Rubio Hervas, Aiguo Song, and Haikun Wei. "Fisher Information Matrix of Unipolar Activation Function-Based Multilayer Perceptrons." IEEE Transactions on Cybernetics 49, no. 8 (August 2019): 3088–98. http://dx.doi.org/10.1109/tcyb.2018.2838680.

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Yan, Junkun, Hongwei Liu, Wenqiang Pu, and Zheng Bao. "Exact Fisher Information Matrix With State-Dependent Probability of Detection." IEEE Transactions on Aerospace and Electronic Systems 53, no. 3 (June 2017): 1555–61. http://dx.doi.org/10.1109/taes.2017.2667418.

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