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Опубліковано: 14 березня 2023

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Статті в журналах з теми "Linear estimation problems"

1

Florens, Jean-Pierre, and Anna Simoni. "REGULARIZING PRIORS FOR LINEAR INVERSE PROBLEMS." Econometric Theory 32, no. 1 (November 6, 2014): 71–121. http://dx.doi.org/10.1017/s0266466614000796.

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This paper proposes a new Bayesian approach for estimating, nonparametrically, functional parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior we propose the posterior mean as an estimator and prove frequentist consistency of the posterior distribution. The latter provides the frequentist validation of our Bayesian procedure. We show that the minimax rate of contraction of the posterior distribution can be obtained provided that either the regularity of the prior matches the regularity of the true parameter or the prior is scaled at an appropriate rate. The scaling parameter of the prior distribution plays the role of a regularization parameter. We propose a new data-driven method for optimally selecting in practice this regularization parameter. We also provide sufficient conditions such that the posterior mean, in a conjugate-Gaussian setting, is equal to a Tikhonov-type estimator in a frequentist setting. Under these conditions our data-driven method is valid for selecting the regularization parameter of the Tikhonov estimator as well. Finally, we apply our general methodology to two leading examples in econometrics: instrumental regression and functional regression estimation.
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2

del Álamo, Miguel, and Axel Munk. "Total variation multiscale estimators for linear inverse problems." Information and Inference: A Journal of the IMA 9, no. 4 (March 2, 2020): 961–86. http://dx.doi.org/10.1093/imaiai/iaaa001.

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Abstract Even though the statistical theory of linear inverse problems is a well-studied topic, certain relevant cases remain open. Among these is the estimation of functions of bounded variation ($BV$), meaning $L^1$ functions on a $d$-dimensional domain whose weak first derivatives are finite Radon measures. The estimation of $BV$ functions is relevant in many applications, since it involves minimal smoothness assumptions and gives simplified, interpretable cartoonized reconstructions. In this paper, we propose a novel technique for estimating $BV$ functions in an inverse problem setting and provide theoretical guaranties by showing that the proposed estimator is minimax optimal up to logarithms with respect to the $L^q$-risk, for any $q\in [1,\infty )$. This is to the best of our knowledge the first convergence result for $BV$ functions in inverse problems in dimension $d\geq 2$, and it extends the results of Donoho (1995, Appl. Comput. Harmon. Anal., 2, 101–126) in $d=1$. Furthermore, our analysis unravels a novel regime for large $q$ in which the minimax rate is slower than $n^{-1/(d+2\beta +2)}$, where $\beta$ is the degree of ill-posedness: our analysis shows that this slower rate arises from the low smoothness of $BV$ functions. The proposed estimator combines variational regularization techniques with the wavelet-vaguelette decomposition of operators.
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3

Ross, G. J. S. "Estimation problems of non-linear functional relationships." Journal of Applied Statistics 17, no. 3 (January 1990): 299–306. http://dx.doi.org/10.1080/02664769000000002.

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4

Koo, Ja-Yong, and Han-Yeong Chung. "Log-density estimation in linear inverse problems." Annals of Statistics 26, no. 1 (February 1998): 335–62. http://dx.doi.org/10.1214/aos/1030563989.

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5

Volaufová, Júlia. "Some estimation problems in multistage linear models." Linear Algebra and its Applications 388 (September 2004): 389–97. http://dx.doi.org/10.1016/j.laa.2004.03.007.

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6

Adjali, M. H., and M. Laurent. "Thermal conductivity estimation in non-linear problems." International Journal of Heat and Mass Transfer 50, no. 23-24 (November 2007): 4623–28. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.03.005.

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7

Ran, Mengfei, and Yihe Yang. "Optimal Estimation of Large Functional and Longitudinal Data by Using Functional Linear Mixed Model." Mathematics 10, no. 22 (November 17, 2022): 4322. http://dx.doi.org/10.3390/math10224322.

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The estimation of large functional and longitudinal data, which refers to the estimation of mean function, estimation of covariance function, and prediction of individual trajectory, is one of the most challenging problems in the field of high-dimensional statistics. Functional Principal Components Analysis (FPCA) and Functional Linear Mixed Model (FLMM) are two major statistical tools used to address the estimation of large functional and longitudinal data; however, the former suffers from a dramatically increasing computational burden while the latter does not have clear asymptotic properties. In this paper, we propose a computationally effective estimator of large functional and longitudinal data within the framework of FLMM, in which all the parameters can be automatically estimated. Under certain regularity assumptions, we prove that the mean function estimation and individual trajectory prediction reach the minimax lower bounds of all nonparametric estimations. Through numerous simulations and real data analysis, we show that our new estimator outperforms the traditional FPCA in terms of mean function estimation, individual trajectory prediction, variance estimation, covariance function estimation, and computational effectiveness.
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8

ODEN, J. TINSLEY, SERGE PRUDHOMME, TIM WESTERMANN, JON BASS, and MARK E. BOTKIN. "ERROR ESTIMATION OF EIGENFREQUENCIES FOR ELASTICITY AND SHELL PROBLEMS." Mathematical Models and Methods in Applied Sciences 13, no. 03 (March 2003): 323–44. http://dx.doi.org/10.1142/s0218202503002520.

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In this paper, a method for deriving computable estimates of the approximation error in eigenvalues or eigenfrequencies of three-dimensional linear elasticity or shell problems is presented. The analysis for the error estimator follows the general approach of goal-oriented error estimation for which the error is estimated in so-called quantities of interest, here the eigenfrequencies, rather than global norms. A general theory is developed and is then applied to the linear elasticity equations. For the shell analysis, it is assumed that the shell model is not completely known and additional errors are introduced due to modeling approximations. The approach is then based on recovering three-dimensional approximations from the shell eigensolution and employing the error estimator developed for linear elasticity. The performance of the error estimator is demonstrated on several test problems.
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9

С. И., Носков,, and Базилевский, М. П. "Multiple Lv-estimation of Linear Regression Models." Успехи кибернетики / Russian Journal of Cybernetics, no. 4(12) (December 28, 2022): 32–40. http://dx.doi.org/10.51790/2712-9942-2022-3-4-04.

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для оценки моделей множественной линейной регрессии существует много различных математических методов: наименьших квадратов, модулей, антиробастного оценивания, Lv-оценивания, множественного оценивания. Целью данной работы является обобщение указанных методов оценивания единой функцией потерь. Сначала была сформулирована задача оценивания, в которой в качестве критериев минимизации выступают критерии для антиробастного и Lv-оценивания. Недостатком сформулированной задачи является то, что для ее численного решения затруднительно определять начальные значения параметров, поскольку переменные могут иметь разные масштабы. Кроме того, функция потерь для этой задачи является неоднородной, что также затрудняет процесс оценивания. Для решения этих проблем введен новый критерий, равный критерию антиробастного оценивания, возведенному в степень v. С помощью него и функции потерь для Lv-оценивания сформулирована задача множественного Lv-оценивания. Функционал этой задачи является однородным, поэтому для проведения множественного Lv-оценивания целесообразно нормировать исходные переменные и переходить к оценкам стандартизованной линейной регрессии. Предложен алгоритм, по которому рекомендуется проводить множественное Lv-оценивание. В результате проведения множественного Lv-оценивания формируется множество, содержащее оценки линейной регрессии, полученные как известными методами, так и новыми. Правильный выбор наилучших из полученного множества оценок пока остается открытой научной задачей. С помощью предложенного множественного Lv-оценивания успешно решена задача моделирования железнодорожных пассажирских перевозок Иркутской области. there are many methods for estimating multiple linear regression models: ordinary least squares, least absolute deviations, anti-robust estimation, Lv-estimation, and multiple estimations. The purpose of this work is to generalize these methods by a loss function. First, an estimation problem was formulated where the minimization criteria are the anti-robust and Lv-estimations. The disadvantage of this problem statement is that it is difficult to determine the initial values of the parameters for a numerical solution, since the variables may have different scales. Besides, the loss function is non-uniform, which also complicates the estimation. To solve these problems, we introduced a new criterion, equal to the anti-robust estimation criterion raised to the power v. We stated the problem of multiple Lv-estimation using the new criterion and the loss function. The functional of this problem is homogeneous, therefore, for multiple Lv-estimations, it is advisable to normalize the initial variables and then apply the standardized linear regression estimates. We also developed an algorithm for multiple Lv-estimations. A result of such estimations is a set containing linear regression estimates obtained both by the existing and new methods. The optimal choice of the best estimates from the set of estimates remains an open problem. We successfully simulated the passenger railway traffic in the Irkutsk region with the proposed multiple Lv-estimations.
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10

Endtmayer, Bernhard, Ulrich Langer, and Thomas Wick. "Multigoal-oriented error estimates for non-linear problems." Journal of Numerical Mathematics 27, no. 4 (December 18, 2019): 215–36. http://dx.doi.org/10.1515/jnma-2018-0038.

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Abstract In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the Partial Differential Equation (PDE) and the goal functionals may be nonlinear. Our method is based on a posteriori error estimates in which the adjoint problem is used and a partition-of-unity is employed for the error localization that allows us to formulate the error estimator in the weak form. We provide a careful derivation of the primal and adjoint parts of the error estimator. The second objective is concerned with balancing the nonlinear iteration error with the discretization error yielding adaptive stopping rules for Newton’s method. Our techniques are substantiated with several numerical examples including scalar PDEs and PDE systems, geometric singularities, and both nonlinear PDEs and nonlinear goal functionals. In these tests, up to six goal functionals are simultaneously controlled.
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Дисертації з теми "Linear estimation problems"

1

Edlund, Ove. "Solution of linear programming and non-linear regression problems using linear M-estimation methods /." Luleå, 1999. http://epubl.luth.se/1402-1544/1999/17/index.html.

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2

PIEROPAN, MIRKO. "Expectation Propagation Methods for Approximate Inference in Linear Estimation Problems." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2918002.

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3

Kaperick, Bryan James. "Diagonal Estimation with Probing Methods." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/90402.

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Probing methods for trace estimation of large, sparse matrices has been studied for several decades. In recent years, there has been some work to extend these techniques to instead estimate the diagonal entries of these systems directly. We extend some analysis of trace estimators to their corresponding diagonal estimators, propose a new class of deterministic diagonal estimators which are well-suited to parallel architectures along with heuristic arguments for the design choices in their construction, and conclude with numerical results on diagonal estimation and ordering problems, demonstrating the strengths of our newly-developed methods alongside existing methods.
Master of Science
In the past several decades, as computational resources increase, a recurring problem is that of estimating certain properties very large linear systems (matrices containing real or complex entries). One particularly important quantity is the trace of a matrix, defined as the sum of the entries along its diagonal. In this thesis, we explore a problem that has only recently been studied, in estimating the diagonal entries of a particular matrix explicitly. For these methods to be computationally more efficient than existing methods, and with favorable convergence properties, we require the matrix in question to have a majority of its entries be zero (the matrix is sparse), with the largest-magnitude entries clustered near and on its diagonal, and very large in size. In fact, this thesis focuses on a class of methods called probing methods, which are of particular efficiency when the matrix is not known explicitly, but rather can only be accessed through matrix vector multiplications with arbitrary vectors. Our contribution is new analysis of these diagonal probing methods which extends the heavily-studied trace estimation problem, new applications for which probing methods are a natural choice for diagonal estimation, and a new class of deterministic probing methods which have favorable properties for large parallel computing architectures which are becoming ever-more-necessary as problem sizes continue to increase beyond the scope of single processor architectures.
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4

Schülke, Christophe. "Statistical physics of linear and bilinear inference problems." Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC058.

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Le développement récent de l'acquisition comprimée a permis de spectaculaires avancées dans la compréhension des problèmes d'estimation linéaire parcimonieuse. Ce développement a suscité un intérêt renouvelé pour les problèmes d'inférence linéaire et bilinéaire généralisée. Ces problèmes combinent une étape linéaire avec une étape non lineaire et probabiliste, à l'issue de laquelle des mesures sont effectuées. Ce type de situations se présente notamment en imagerie médicale et en astronomie. Cette thèse s'intéresse à des algorithmes pour la résolution de ces problèmes et à leur analyse théorique. Pour cela, nous utilisons des algorithmes de passage de message, qui permettent d'échantillonner des distributions de haute dimension. Ces algorithmes connaissent des changements de phase, qui se laissent analyser à l'aide de la méthode des répliques, initialement développée dans le cadre de la physique statistique des milieux désordonnés. L'analyse des phases révèle qu'elles correspondent à des domaines dans lesquels l'inférence est facile, difficile ou impossible. Les principales contributions de cette thèse sont de trois types. D'abord, l'application d'algorithmes connus à des problèmes concrets : détection de communautés, codes correcteurs d'erreurs ainsi qu'un système d'imagerie innovant. Ensuite, un nouvel algorithme traitant le problème de calibration aveugle de capteurs, potentiellement applicable à de nombreux systèmes de mesure. Enfin, une analyse théorique du problème de reconstruction de matrices à petit rang à partir de projections linéaires, ainsi qu'une analyse d'une instabilité présente dans les algorithmes d'inférence bilinéaire
The recent development of compressed sensing has led to spectacular advances in the under standing of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered anew wave of developments in the related fields of generalized linear and bilinear inference problems. These problems have in common that they combine a linear mixing step and a nonlinear, probabilistic sensing step, producing indirect measurements of a signal of interest. Such a setting arises in problems such as medical or astronomical Imaging. The aim of this thesis is to propose efficient algorithms for this class of problems and to perform their theoretical analysis. To this end, it uses belief propagation, thanks to which high-dimensional distributions can be sampled efficiently, thus making a bayesian approach to inference tractable. The resulting algorithms undergo phase transitions that can be analyzed using the replica method, initially developed in statistical physics of disordered systems. The analysis reveals phases in which inference is easy, hard or impossible, corresponding to different energy landscapes of the problem. The main contributions of this thesis can be divided into three categories. First, the application of known algorithms to concrete problems : community detection, superposition codes and an innovative imaging system. Second, a new, efficient message-passing algorithm for blind sensor calibration, that could be used in signal processing for a large class of measurement systems. Third, a theoretical analysis of achievable performances in matrix compressed sensing and of instabilities in bayesian bilinear inference algorithms
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5

Mattavelli, Marco Mattavelli Marco Mattavelli Marco. "Motion analysis and estimation : from III-posed discrete linear inverse problems to MPEG-2 coding /." Lausanne, 1997. http://library.epfl.ch/theses/?nr=1596.

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Thèse, Sciences techniques, EPF Lausanne, No 1596, 1997, Section de systèmes de communication. Rapporteur: M. Kunt ; Co-rapporteur: B. Macq ; Co-rapporteur: D. Mlynek ; Co-rapporteur: F. Pellandini.
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6

Barbier, Jean. "Statistical physics and approximate message-passing algorithms for sparse linear estimation problems in signal processing and coding theory." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC130.

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Cette thèse s’intéresse à l’application de méthodes de physique statistique des systèmes désordonnés ainsi que de l’inférence à des problèmes issus du traitement du signal et de la théorie du codage, plus précisément, aux problèmes parcimonieux d’estimation linéaire. Les outils utilisés sont essentiellement les modèles graphiques et l’algorithme approximé de passage de messages ainsi que la méthode de la cavité (appelée analyse de l’évolution d’état dans le contexte du traitement de signal) pour son analyse théorique. Nous aurons également recours à la méthode des répliques de la physique des systèmes désordonnées qui permet d’associer aux problèmes rencontrés une fonction de coût appelé potentiel ou entropie libre en physique. Celle-ci permettra de prédire les différentes phases de complexité typique du problème, en fonction de paramètres externes tels que le niveau de bruit ou le nombre de mesures liées au signal auquel l’on a accès : l’inférence pourra être ainsi typiquement simple, possible mais difficile et enfin impossible. Nous verrons que la phase difficile correspond à un régime où coexistent la solution recherchée ainsi qu’une autre solution des équations de passage de messages. Dans cette phase, celle-ci est un état métastable et ne représente donc pas l’équilibre thermodynamique. Ce phénomène peut-être rapproché de la surfusion de l’eau, bloquée dans l’état liquide à une température où elle devrait être solide pour être à l’équilibre. Via cette compréhension du phénomène de blocage de l’algorithme, nous utiliserons une méthode permettant de franchir l’état métastable en imitant la stratégie adoptée par la nature pour la surfusion : la nucléation et le couplage spatial. Dans de l’eau en état métastable liquide, il suffit d’une légère perturbation localisée pour que se créer un noyau de cristal qui va rapidement se propager dans tout le système de proche en proche grâce aux couplages physiques entre atomes. Le même procédé sera utilisé pour aider l’algorithme à retrouver le signal, et ce grâce à l’introduction d’un noyau contenant de l’information locale sur le signal. Celui-ci se propagera ensuite via une "onde de reconstruction" similaire à la propagation de proche en proche du cristal dans l’eau. Après une introduction à l’inférence statistique et aux problèmes d’estimation linéaires, on introduira les outils nécessaires. Seront ensuite présentées des applications de ces notions. Celles-ci seront divisées en deux parties. La partie traitement du signal se concentre essentiellement sur le problème de l’acquisition comprimée où l’on cherche à inférer un signal parcimonieux dont on connaît un nombre restreint de projections linéaires qui peuvent être bruitées. Est étudiée en profondeur l’influence de l’utilisation d’opérateurs structurés à la place des matrices aléatoires utilisées originellement en acquisition comprimée. Ceux-ci permettent un gain substantiel en temps de traitement et en allocation de mémoire, conditions nécessaires pour le traitement algorithmique de très grands signaux. Nous verrons que l’utilisation combinée de tels opérateurs avec la méthode du couplage spatial permet d’obtenir un algorithme de reconstruction extrê- mement optimisé et s’approchant des performances optimales. Nous étudierons également le comportement de l’algorithme confronté à des signaux seulement approximativement parcimonieux, question fondamentale pour l’application concrète de l’acquisition comprimée sur des signaux physiques réels. Une application directe sera étudiée au travers de la reconstruction d’images mesurées par microscopie à fluorescence. La reconstruction d’images dites "naturelles" sera également étudiée. En théorie du codage, seront étudiées les performances du décodeur basé sur le passage de message pour deux modèles distincts de canaux continus. Nous étudierons un schéma où le signal inféré sera en fait le bruit que l’on pourra ainsi soustraire au signal reçu. Le second, les codes de superposition parcimonieuse pour le canal additif Gaussien est le premier exemple de schéma de codes correcteurs d’erreurs pouvant être directement interprété comme un problème d’acquisition comprimée structuré. Dans ce schéma, nous appliquerons une grande partie des techniques étudiée dans cette thèse pour finalement obtenir un décodeur ayant des résultats très prometteurs à des taux d’information transmise extrêmement proches de la limite théorique de transmission du canal
This thesis is interested in the application of statistical physics methods and inference to signal processing and coding theory, more precisely, to sparse linear estimation problems. The main tools are essentially the graphical models and the approximate message-passing algorithm together with the cavity method (referred as the state evolution analysis in the signal processing context) for its theoretical analysis. We will also use the replica method of statistical physics of disordered systems which allows to associate to the studied problems a cost function referred as the potential of free entropy in physics. It allows to predict the different phases of typical complexity of the problem as a function of external parameters such as the noise level or the number of measurements one has about the signal: the inference can be typically easy, hard or impossible. We will see that the hard phase corresponds to a regime of coexistence of the actual solution together with another unwanted solution of the message passing equations. In this phase, it represents a metastable state which is not the true equilibrium solution. This phenomenon can be linked to supercooled water blocked in the liquid state below its freezing critical temperature. Thanks to this understanding of blocking phenomenon of the algorithm, we will use a method that allows to overcome the metastability mimicing the strategy adopted by nature itself for supercooled water: the nucleation and spatial coupling. In supercooled water, a weak localized perturbation is enough to create a crystal nucleus that will propagate in all the medium thanks to the physical couplings between closeby atoms. The same process will help the algorithm to find the signal, thanks to the introduction of a nucleus containing local information about the signal. It will then spread as a "reconstruction wave" similar to the crystal in the water. After an introduction to statistical inference and sparse linear estimation, we will introduce the necessary tools. Then we will move to applications of these notions. They will be divided into two parts. The signal processing part will focus essentially on the compressed sensing problem where we seek to infer a sparse signal from a small number of linear projections of it that can be noisy. We will study in details the influence of structured operators instead of purely random ones used originally in compressed sensing. These allow a substantial gain in computational complexity and necessary memory allocation, which are necessary conditions in order to work with very large signals. We will see that the combined use of such operators with spatial coupling allows the implementation of an highly optimized algorithm able to reach near to optimal performances. We will also study the algorithm behavior for reconstruction of approximately sparse signals, a fundamental question for the application of compressed sensing to real life problems. A direct application will be studied via the reconstruction of images measured by fluorescence microscopy. The reconstruction of "natural" images will be considered as well. In coding theory, we will look at the message-passing decoding performances for two distincts real noisy channel models. A first scheme where the signal to infer will be the noise itself will be presented. The second one, the sparse superposition codes for the additive white Gaussian noise channel is the first example of error correction scheme directly interpreted as a structured compressed sensing problem. Here we will apply all the tools developed in this thesis for finally obtaining a very promising decoder that allows to decode at very high transmission rates, very close of the fundamental channel limit
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7

Krishnan, Rajet. "Problems in distributed signal processing in wireless sensor networks." Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1351.

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8

Kontak, Max [Verfasser]. "Novel algorithms of greedy-type for probability density estimation as well as linear and nonlinear inverse problems / Max Kontak." Siegen : Universitätsbibliothek der Universität Siegen, 2018. http://d-nb.info/1157094554/34.

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9

Pester, Cornelia. "A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularities." Doctoral thesis, Berlin Logos-Verl, 2006. http://deposit.ddb.de/cgi-bin/dokserv?id=2806614&prov=M&dok_var=1&dok_ext=htm.

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10

Pester, Cornelia. "A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularities." Doctoral thesis, Logos Verlag Berlin, 2005. https://monarch.qucosa.de/id/qucosa%3A18520.

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Анотація:
This thesis is concerned with the finite element analysis and the a posteriori error estimation for eigenvalue problems for general operator pencils on two-dimensional manifolds. A specific application of the presented theory is the computation of corner singularities. Engineers use the knowledge of the so-called singularity exponents to predict the onset and the propagation of cracks. All results of this thesis are explained for two model problems, the Laplace and the linear elasticity problem, and verified by numerous numerical results.
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Книги з теми "Linear estimation problems"

1

Kontoghiorghes, Erricos John. Parallel algorithms for linear models: Numerical methods and estimation problems. Boston: Kluwer Academic, 2000.

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2

Hesselager, Ole. On the application of bootstrap in some empirical linear bayes estimation problems. Copenhagen: University of Copenhagen, 1988.

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3

Pester, Cornelia. A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularities. Berlin: Logos-Verl., 2006.

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4

M, Milanese, ed. Bounding approaches to system identification. New York: Plenum Press, 1996.

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5

1975-, Sims Robert, and Ueltschi Daniel 1969-, eds. Entropy and the quantum II: Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Providence, R.I: American Mathematical Society, 2011.

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6

Parallel Algorithms for Linear Models: Numerical Methods and Estimation Problems. Springer, 2011.

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7

Kontoghiorghes, Erricos. Parallel Algorithms for Linear Models: Numerical Methods and Estimation Problems. Springer London, Limited, 2012.

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8

Cardot, Hervé, and Pascal Sarda. Functional Linear Regression. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.2.

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This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.
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9

Nakonechnyi, Oleksandr, and Yuri Podlipenko. Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data. River Publishers, 2021.

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10

Nakonechnyi, Oleksandr, and Yuri Podlipenko. Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data. River Publishers, 2022.

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Частини книг з теми "Linear estimation problems"

1

Grafarend, Erik W., and Joseph L. Awange. "Special Problems of Algebraic Regression and Stochastic Estimation." In Linear and Nonlinear Models, 493–525. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22241-2_14.

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2

Griffith, Daniel A., and Jean H. P. Paelinck. "Linear Expenditure Systems and Related Estimation Problems." In Advanced Studies in Theoretical and Applied Econometrics, 201–13. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72553-6_17.

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3

Grafarend, Erik, Silvelyn Zwanzig, and Joseph Awange. "Special Problems of Algebraic Regression and Stochastic Estimation." In Applications of Linear and Nonlinear Models, 499–531. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94598-5_14.

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4

Pillonetto, Gianluigi, Tianshi Chen, Alessandro Chiuso, Giuseppe De Nicolao, and Lennart Ljung. "Regularization in Reproducing Kernel Hilbert Spaces for Linear System Identification." In Regularized System Identification, 247–311. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95860-2_7.

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AbstractIn the previous parts of the book, we have studied how to handle linear system identification by using regularized least squares (ReLS) with finite-dimensional structures given, e.g., by finite impulse response (FIR) models. In this chapter, we cast this approach in the RKHS framework developed in the previous chapter. We show that ReLS with quadratic penalties can be reformulated as a function estimation problem in the finite-dimensional RKHS induced by the regularization matrix. This leads to a new paradigm for linear system identification that provides also new insights and regularization tools to handle infinite-dimensional problems, involving, e.g., IIR and continuous-time models. For all this class of problems, we will see that the representer theorem ensures that the regularized impulse response is a linear and finite combination of basis functions given by the convolution between the system input and the kernel sections. We then consider the issue of kernel estimation and introduce several tuning methods that have close connections with those related to the regularization matrix discussed in Chap. 10.1007/978-3-030-95860-2_3. Finally, we introduce the notion of stable kernels, that induce RKHSs containing only absolutely summable impulse responses and study minimax properties of regularized impulse response estimation.
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5

Dobra, Adrian, Stephen E. Fienberg, Alessandro Rinaldo, Aleksandra Slavkovic, and Yi Zhou. "Algebraic Statistics and Contingency Table Problems: Log-Linear Models, Likelihood Estimation, and Disclosure Limitation." In Emerging Applications of Algebraic Geometry, 63–88. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-09686-5_3.

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6

Nakonechnyi, O., and Y. Podlipenko. "Guaranteed Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with General Boundary Data." In Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data, 163–216. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003338369-4.

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7

Nakonechnyi, O., and Y. Podlipenko. "Guaranteed Estimation of Unknown Solutions and Right-Hand Sides of First Order Linear Systems of Periodic ODEs." In Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data, 79–102. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003338369-2.

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8

Nakonechnyi, O., and Y. Podlipenko. "Guaranteed Estimation of Solutions of Boundary Value Problems for Linear Ordinary Differential Equations with Decomposed Boundary Data." In Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data, 103–62. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003338369-3.

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9

Nakonechnyi, O., and Y. Podlipenko. "Guaranteed Estimates of Solutions and Right-Hand Sides of the Cauchy Problem Under Incomplete Data." In Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data, 5–77. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003338369-1.

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10

Korotov, Sergey, Pekka Neittaanmäki, and Sergey Repin. "A Posteriori Error Estimation in Terms of Linear Functionals for Boundary Value Problems of Elliptic Type." In Numerical Mathematics and Advanced Applications, 587–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18775-9_56.

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Тези доповідей конференцій з теми "Linear estimation problems"

1

Van Wijk, K., J. A. Scales, and W. Navidi. "Uncertainty Estimation and Error Analysis for Linear Inversion Problems." In 63rd EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2001. http://dx.doi.org/10.3997/2214-4609-pdb.15.n-33.

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2

Fuhrmann, Daniel R. "One-step optimal measurement selection for linear gaussian estimation problems." In 2007 International Waveform Diversity and Design Conference. IEEE, 2007. http://dx.doi.org/10.1109/wddc.2007.4339415.

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3

Annaswamy, A. M., C. Thanomsat, N. R. Mehta, and A. P. Loh. "A New Approach to Estimation of Nonlinear Parametrization in Dynamic Systems." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0398.

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Abstract Nonlinear parametrizations occur in dynamic models of several complex engineering problems. The theory of adaptive estimation and control has been applicable, by and large, to problems where parameters appear linearly. We have recently developed an adaptive controller that is capable of estimating parameters that appear nonlinearly in dynamic systems in a stable manner. In this paper, we present this algorithm and its applicability to the problem of temperature regulation in chemical reactors. It is shown in that the proposed controller leads to a significantly better performance than those based on linear parametrizations.
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4

Ikami, Daiki, Toshihiko Yamasaki, and Kiyoharu Aizawa. "Fast and Robust Estimation for Unit-Norm Constrained Linear Fitting Problems." In 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2018. http://dx.doi.org/10.1109/cvpr.2018.00850.

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5

Suliman, Mohamed A., Houssem Sifaou, Tarig Ballal, Mohamed-Slim Alouini, and Tareq Y. Al-Naffouri. "Robust Estimation in Linear ILL-Posed Problems with Adaptive Regularization Scheme." In ICASSP 2018 - 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018. http://dx.doi.org/10.1109/icassp.2018.8462651.

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6

Ito, Yoshimichi, Katsumi Irie, and Shun Otsuka. "Estimation of geometric parameters in 3D reconstruction problems using linear matrix inequalities." In 2014 Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS) and 15th International Symposium on Advanced Intelligent Systems (ISIS). IEEE, 2014. http://dx.doi.org/10.1109/scis-isis.2014.7044790.

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7

Volkov, Vasiliy, and Dmitriy Demyanov. "Optimal Estimation of the Linear Functional of State Variables of a Dynamic System." In 2019 XXI International Conference Complex Systems: Control and Modeling Problems (CSCMP). IEEE, 2019. http://dx.doi.org/10.1109/cscmp45713.2019.8976873.

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8

Liu, Zhaoqiang, and Jun Han. "Projected Gradient Descent Algorithms for Solving Nonlinear Inverse Problems with Generative Priors." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/454.

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In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown signal lies near the range of a Lipschitz continuous generative model with bounded inputs. In particular, we consider two cases when the nonlinear link function is either unknown or known. For unknown nonlinearity, we make the assumption of sub-Gaussian observations and propose a linear least-squares estimator. We show that when there is no representation error, the sensing vectors are Gaussian, and the number of samples is sufficiently large, with high probability, a PGD algorithm converges linearly to a point achieving the optimal statistical rate using arbitrary initialization. For known nonlinearity, we assume monotonicity, and make much weaker assumptions on the sensing vectors and allow for representation error. We propose a nonlinear least-squares estimator that is guaranteed to enjoy an optimal statistical rate. A corresponding PGD algorithm is provided and is shown to also converge linearly to the estimator using arbitrary initialization. In addition, we present experimental results on image datasets to demonstrate the performance of our PGD algorithms.
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9

Hill, David C. "Identification of Gas Turbine Dynamics: Time-Domain Estimation Problems." In ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/97-gt-031.

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The characteristic form of a linear gas turbine model is examined. Time domain models are obtained from engine test data. Transfer function model estimates exhibit unrealistic pole positions. This is caused by systematic bias in the parameter estimates, coupled with high sensitivity of the poles to parameter errors. The bias is a result of using a measured fuel flow as the model input. This violates the requirement that the input be piece-wise constant. The problem is reduced using multiple-output state space models, which are less sensitive to small parameter errors.
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10

Chubich, Vladimir M., and Alina E. Prokofeva. "The Application of Robust Estimation to Active Parametric Identification of Stochastic Linear Discrete Systems." In 2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE). IEEE, 2018. http://dx.doi.org/10.1109/apeie.2018.8545985.

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Звіти організацій з теми "Linear estimation problems"

1

Hou, Elizabeth Mary, and Earl Christopher Lawrence. Variational Methods for Posterior Estimation of Non-linear Inverse Problems. Office of Scientific and Technical Information (OSTI), September 2018. http://dx.doi.org/10.2172/1475317.

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2

Ayoul-Guilmard, Q., F. Nobile, S. Ganesh, M. Nuñez, R. Tosi, C. Soriano, and R. Rosi. D5.5 Report on the application of multi-level Monte Carlo to wind engineering. Scipedia, 2022. http://dx.doi.org/10.23967/exaqute.2022.3.03.

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We study the use of multi-level Monte Carlo methods for wind engineering. This report brings together methodological research on uncertainty quantification and work on target applications of the ExaQUte project in wind and civil engineering. First, a multi-level Monte Carlo for the estimation of the conditional value at risk and an adaptive algorithm are presented. Their reliability and performance are shown on the time-average of a non-linear oscillator and on the lift coefficient of an airfoil, with both preset and adaptively refined meshes. Then, we propose an adaptive multi-fidelity Monte Carlo algorithm for turbulent fluid flows where multilevel Monte Carlo methods were found to be inefficient. Its efficiency is studied and demonstrated on the benchmark problem of quantifying the uncertainty on the drag force of a tall building under random turbulent wind conditions. All numerical experiments showcase the open-source software stack of the ExaQUte project for large-scale computing in a distributed environment.
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3

Searcy, Stephen W., and Kalman Peleg. Adaptive Sorting of Fresh Produce. United States Department of Agriculture, August 1993. http://dx.doi.org/10.32747/1993.7568747.bard.

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This project includes two main parts: Development of a “Selective Wavelength Imaging Sensor” and an “Adaptive Classifiery System” for adaptive imaging and sorting of agricultural products respectively. Three different technologies were investigated for building a selectable wavelength imaging sensor: diffraction gratings, tunable filters and linear variable filters. Each technology was analyzed and evaluated as the basis for implementing the adaptive sensor. Acousto optic tunable filters were found to be most suitable for the selective wavelength imaging sensor. Consequently, a selectable wavelength imaging sensor was constructed and tested using the selected technology. The sensor was tested and algorithms for multispectral image acquisition were developed. A high speed inspection system for fresh-market carrots was built and tested. It was shown that a combination of efficient parallel processing of a DSP and a PC based host CPU in conjunction with a hierarchical classification system, yielded an inspection system capable of handling 2 carrots per second with a classification accuracy of more than 90%. The adaptive sorting technique was extensively investigated and conclusively demonstrated to reduce misclassification rates in comparison to conventional non-adaptive sorting. The adaptive classifier algorithm was modeled and reduced to a series of modules that can be added to any existing produce sorting machine. A simulation of the entire process was created in Matlab using a graphical user interface technique to promote the accessibility of the difficult theoretical subjects. Typical Grade classifiers based on k-Nearest Neighbor techniques and linear discriminants were implemented. The sample histogram, estimating the cumulative distribution function (CDF), was chosen as a characterizing feature of prototype populations, whereby the Kolmogorov-Smirnov statistic was employed as a population classifier. Simulations were run on artificial data with two-dimensions, four populations and three classes. A quantitative analysis of the adaptive classifier's dependence on population separation, training set size, and stack length determined optimal values for the different parameters involved. The technique was also applied to a real produce sorting problem, e.g. an automatic machine for sorting dates by machine vision in an Israeli date packinghouse. Extensive simulations were run on actual sorting data of dates collected over a 4 month period. In all cases, the results showed a clear reduction in classification error by using the adaptive technique versus non-adaptive sorting.
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4

Mayfield, Colin. Capacity Development in the Water Sector: the case of Massive Open On-line Courses. United Nations University Institute for Water, Environment and Health, January 2017. http://dx.doi.org/10.53328/mwud6984.

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Анотація:
The Sustainable Development Goal 6 targets are all dependent on capacity development as outlined in SDG 6a “Expand international cooperation and capacity-building support to developing countries in water- and sanitation related activities and programmes “. Massive Open On-line Courses (MOOCs) and distance learning in general have a significant role to play in this expansion. This report examines the role that MOOCs and similar courses could play in capacity development in the water sector. The appearance of MOOCs in 2010/11 led within 4 years to a huge increase in this type of course and in student enrollment. Some problems with student dropout rates, over-estimating the transformational and disruptive nature of MOOCs and uncertain business models remain, but less “massive” MOOCs with more engaged students are overcoming these problems. There are many existing distance learning courses and programmes in the water sector designed to train and/ or educate professionals, operators, graduate and undergraduate students and, to a lesser extent, members of communities dealing with water issues. There are few existing true MOOCs in the water sector. MOOCs could supply significant numbers of qualified practitioners for the water sector. A suite of programmes on water-related topics would allow anyone to try the courses and determine whether they were appropriate and useful. If they were, the students could officially enroll in the course or programme to gain a meaningful qualification or simply to upgrade their qualifications. To make MOOCs more relevant to education and training in the water sector an analysis of the requirements in the sector and the potential demand for such courses is required. Cooperation between institutions preparing MOOCs would be desirable given the substantial time and funding required to produce excellent quality courses. One attractive model for cooperation would be to produce modules on all aspects of water and sanitation dealing with technical, scientific, social, legal and management topics. These should be produced by recognized experts in each field and should be “stand-alone” or complete in themselves. If all modules were made freely available, users or mentors could assemble different MOOCs by linking relevant modules. Then extracts, simplified or less technical versions of the modules could then be used to produce presentations to encourage public participation and for other training purposes. Adaptive learning, where course materials are more tailored to individual students based on their test results and reactions to the material, can be an integral part of MOOCs. MOOCs efficiently provide access to quality courses at low or no cost to students around the world, they enable students to try courses at their convenience, they can be tailored to both professional and technical aspects, and they are very suitable to provide adaptive learning courses. Cooperation between institutions would provide many course modules for the water sector that collectively could provide excellent programmes to address the challenges of capacity development for SDG 6 and other issues within the water sector.
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