Dissertations / Theses on the topic 'Minimax'
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Läuter, Henning. "Empirical Minimax Linear Estimates." Universität Potsdam, 2008. http://opus.kobv.de/ubp/volltexte/2011/4948/.
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Göransson, Marcus Östergren. "Minimax Based Kalaha AI." Thesis, Blekinge Tekniska Högskola, Sektionen för datavetenskap och kommunikation, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-5333.
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To construct an algorithm which does well in a board game, one must take into account the time spent on each move and the ability to evaluate the state of the board. There are multiple ways to handle these issues, but only a few are covered in this analysis. AIs using the algorithms minimax, minimax with alpha-beta pruning and minimax with knowledge-based alpha-beta pruning are being compared when playing Kalaha with a 30 second time limit per move. Each algorithm is in addition paired up with two different methods of evaluating the games state. The first one only compares the amount of counters in each players store, while the second, knowledge-based method, extends this with an evaluation of the counters in play. A tournament was held between the AIs where each match-up played twelve games against each other. The regular minimax algorithm is appearing to be inferior to the improved variations. The knowledge-based alpha-beta pruning is unexpectedly unsuccessful in outperforming the regular alpha-beta pruning and a discussion covers possible errors with the implementation and possible improvements. The knowledge-based evaluation method is appearing to be slightly more successful than the simple variant, but a discussion questions the real usefulness of it when paired with more advanced search algorithms than the ones covered in this study.
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Gayraud, Ghislaine. "Estimation minimax de fonctionnelles du support de la densite et tests minimax associes." Paris 6, 1997. http://www.theses.fr/1997PA066084.
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Premierement, on considere l'estimation de fonctionnelles du support de densite g, a partir de n vecteurs aleatoires x#1,. . . , x#n, n-dimensionnels independants et identiquement distribues admettant une densite de probabilite f. On suppose que le support g est un ensemble inconnu inclu dans 0,1#n, dont la mesure de lebesgue est differente de zero. De plus on suppose que g appartient soit a la classe des fragments notee g soit a la classe des ensembles convexes. En utilisant l'approche minimax asymptotique, on obtient des estimateurs optimaux des fonctionnelles au sens ou ils atteignent la vitesse de convergence minimax. Dans une seconde partie, on s'interesse a tester des hypotheses non-parametriques concernant le support g. En particulier on teste l'hypothese nulle que g est egal a g#0, ou g#0 est un ensemble connu appartenant a g, contre une alternative non-parametrique composee, que g appartient a une classe d'ensembles, obtenue en enlevant a g un voisinage autour de g#0. Le probleme est de determiner asymptotiquement la classe alternative optimale pour laquelle on est capable de tester l'hypothese nulle contre l'alternative en nous fixant une somme d'erreurs de probabilite a , (0,1). Le critere d'optimalite est donne par la theorie minimax.
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Park, Jeffrey. "Some Professionals Play Minimax: A Reexamination of the Minimax Theory in Major League Baseball." Scholarship @ Claremont, 2010. http://scholarship.claremont.edu/cmc_theses/31.
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This paper explores the behavior of Major League Baseball pitchers. We analyze the pitching data from 2007-2010 in order to determine whether their actions follow minimax play. We also examine what the OPS statistic tells us about a pitcher's value.
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Beal, Donald Francis. "The nature of minimax search." Maastricht : Maastricht : Universiteit Maastricht ; University Library, Maastricht University [Host], 1999. http://arno.unimaas.nl/show.cgi?fid=7528.
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Dimi, Jean-Luc. "La régression minimax non linéaire." Paris 6, 1987. http://www.theses.fr/1987PA066339.
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Dimi, Jean-Luc. "La Régression Minimax non linéaire." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb37604699w.
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Nabney, Ian Thomas. "Soluble minimax groups and their representations." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333316.
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BRITO, Jacqueline Félix de. "Teoremas do tipo Minimax e aplicações." Universidade Federal de Campina Grande, 2005. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1125.
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Neste trabalho, mostramos a existência de soluções para a seguinte classe de problemas elípticos: (Para ver a formula ou equação recomendamos o download da dissertação). As principais ferramentas utilizadas são os Teoremas de Deformação, Passo da Montanha e Ponto de Sela.
In this work, we show the existence of solutions for the following class for elliptic problem: (To see the formula or equation we recommend downloading the dissertation). (To see the formula or equation we recommend downloading the dissertation).
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Mukherjee, Rajarshi. "Statistical Inference for High Dimensional Problems." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11516.
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In this dissertation, we study minimax hypothesis testing in high-dimensional regression against sparse alternatives and minimax estimation of average treatment effect in an semiparametric regression with possibly large number of covariates.
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Löfberg, Johan. "Minimax Approaches to Robust Model Predictive Control." Doctoral thesis, Linköpings universitet, Reglerteknik, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-98168.
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Controlling a system with control and state constraints is one of the most important problems in control theory, but also one of the most challenging. Another important but just as demanding topic is robustness against uncertainties in a controlled system. One of the most successful approaches, both in theory and practice, to control constrained systems is model predictive control (MPC). The basic idea in MPC is to repeatedly solve optimization problems on-line to find an optimal input to the controlled system. In recent years, much effort has been spent to incorporate the robustness problem into this framework. The main part of the thesis revolves around minimax formulations of MPC for uncertain constrained linear discrete-time systems. A minimax strategy in MPC means that worst-case performance with respect to uncertainties is optimized. Unfortunately, many minimax MPC formulations yield intractable optimization problems with exponential complexity. Minimax algorithms for a number of uncertainty models are derived in the thesis. These include systems with bounded external additive disturbances, systems with uncertain gain, and systems described with linear fractional transformations. The central theme in the different algorithms is semidefinite relaxations. This means that the minimax problems are written as uncertain semidefinite programs, and then conservatively approximated using robust optimization theory. The result is an optimization problem with polynomial complexity. The use of semidefinite relaxations enables a framework that allows extensions of the basic algorithms, such as joint minimax control and estimation, and approx- imation of closed-loop minimax MPC using a convex programming framework. Additional topics include development of an efficient optimization algorithm to solve the resulting semidefinite programs and connections between deterministic minimax MPC and stochastic risk-sensitive control. The remaining part of the thesis is devoted to stability issues in MPC for continuous-time nonlinear unconstrained systems. While stability of MPC for un-constrained linear systems essentially is solved with the linear quadratic controller, no such simple solution exists in the nonlinear case. It is shown how tools from modern nonlinear control theory can be used to synthesize finite horizon MPC controllers with guaranteed stability, and more importantly, how some of the tech- nical assumptions in the literature can be dispensed with by using a slightly more complex controller.
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Flamm, David Simson. "Control of delay systems for minimax sensitivity." Thesis, Massachusetts Institute of Technology, 1986. http://hdl.handle.net/1721.1/15082.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING
Vita.
Bibliography: leaves 161-162.
by David S. Flamm.
Ph.D.
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Yoo, CheolWoo 1962. "Minimax IFIR filter design using subband decomposition." Thesis, The University of Arizona, 1991. http://hdl.handle.net/10150/558157.
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Collier, Olivier. "Méthodes statistiques pour la mise en correspondance de descripteurs." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00904686.
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De nombreuses applications, en vision par ordinateur ou en médecine notamment,ont pour but d'identifier des similarités entre plusieurs images ou signaux. On peut alors détecter des objets, les suivre, ou recouper des prises de vue. Dans tous les cas, les procédures algorithmiques qui traitent les images utilisent une sélection de points-clefs qu'elles essayent ensuite de mettre en correspondance par paire. Elles calculent pour chaque point un descripteur qui le caractérise, le discrimine des autres. Parmi toutes les procédures possibles,la plus utilisée aujourd'hui est SIFT, qui sélectionne les points-clefs, calcule des descripteurs et propose un critère de mise en correspondance globale. Dans une première partie, nous tentons d'améliorer cet algorithme en changeant le descripteur original qui nécessite de trouver l'argument du maximum d'un histogramme : en effet, son calcul est statistiquement instable. Nous devons alors également changer le critère de mise en correspondance de deux descripteurs. Il en résulte un problème de test non paramétrique dans lequel à la fois l'hypothèse nulle et alternative sont composites, et même non paramétriques. Nous utilisons le test du rapport de vraisemblance généralisé afin d'exhiber des procédures de test consistantes, et proposons une étude minimax du problème. Dans une seconde partie, nous nous intéressons à l'optimalité d'une procédure globale de mise en correspondance. Nous énonçons un modèle statistique dans lequel des descripteurs sont présents dans un certain ordre dans une première image, et dans un autre dans une seconde image. La mise en correspondance revient alors à l'estimation d'une permutation. Nous donnons un critère d'optimalité au sens minimax pour les estimateurs. Nous utilisons en particulier la vraisemblance afin de trouver plusieurs estimateurs consistants, et même optimaux sous certaines conditions. Enfin, nous nous sommes intéressés à des aspects pratiques en montrant que nos estimateurs étaient calculables en temps raisonnable, ce qui nous a permis ensuite d'illustrer la hiérarchie de nos estimateurs par des simulations
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Wattanawaroon, Tana. "Local versus global tables in Minimax Game Search." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/92088.
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Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (page 33).
Minimax Game Search with alpha-beta pruning can utilize heuristic tables in order to prune more branches and achieve better performance. The tables can be implemented using different memory models: global tables, worker-local tables and processor-local tables. Depending on whether each heuristic table depends on locality in the game tree, a memory model might be more suitable than others. This thesis describes an experiment that shows that local tables are generally preferable to global tables for two game heuristics used in chess-like games: killer move and best move history. The experiment is evidence that local tables might be useful for multithreaded applications, particularly ones that involve caching and exhibit locality.
by Tana Wattanawaroon.
M. Eng.
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SANTOS, Jefferson Abrantes dos. "Teoremas minimax para funcionais localmente Lipschitz e aplicações." Universidade Federal de Campina Grande, 2007. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1191.
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CNPq
Capes
Neste trabalho estudamos a existência de solução não nula, via Métodos Variacionais para uma classe de problemas Elípticos onde f :R→R apresenta uma descontinuidade, do tipo salto, com seu conjunto de pontos de descontinuidade sendo um conjunto enumerável sem pontos de acumulação e Ω é um domínio limitado com fronteira suave. * Para Visualisar as equações ou formulas originalmente escritas neste resumo recomendamos o downloado do arquivo completo.
In this work we study the existence of solutions for the following class of Elliptic problems wherethefunctionf :R →RhassomediscontinuitiesandΩisaboundeddomainwith smooth boundary. The main tool used is the Variational Methods together arguments developed by Chang [9]. *To see the equations or formulas originally written in this summary we recommend downloading the complete file.
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Sepúlveda, Ariel. "The Minimax control chart for multivariate quality control." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/30230.
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Löfberg, Johan. "Minimax approaches to robust model predictive control / Johan Löfberg." Linköping : Univ, 2003. http://www.bibl.liu.se/liupubl/disp/disp2003/tek812s.pdf.
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VIENNET, GABRIELLE. "Estimation minimax et adaptative dans un cadre absolument régulier." Paris 11, 1996. http://www.theses.fr/1996PA112017.
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Cette these est consacree a l'etude de certains estimateurs non parametriques d'une densite ou d'une fonction de regression lorsque les observations sont stationnaires mais non necessairement independantes. Nous nous attacherons a montrer que la notion de melange que l'on appelle absolue regularite fournit un cadre probabiliste convenable pour mettre en lumiere la robustesse des methodes d'estimation envisagees vis a vis d'une faible perturbation de l'independance des donnees. Plus precisement, le probleme consiste a estimer une fonction s a partir de n observations issues d'un processus stationnaire absolument regulier. S represente soit la densite stationnaire, soit la fonction de regression si on observe un couple de variables aleatoires. Tout d'abord, en faisant des hypotheses a priori sur la fonction s du type s a support compact dans un espace de besov, nous etudions les vitesses de convergence d'estimateurs lineaires (tels les estimateurs a noyau ou par projection) et de certains estimateurs par minimum de contraste sur cribles. Sous une faible condition sommatoire sur les coefficients de melange, les vitesses obtenues sont les memes que celles connues comme etant optimales dans le cas independant. Les demonstrations sont basees sur deux resultats probabilistes importants: une nouvelle inegalite de covariance et une inegalite de moment type rosenthal. Nous etudions ensuite des resultats d'estimation adaptative permettant de s'affranchir des hypotheses a priori concernant la regularite de s. Nous proposons deux estimateurs de la densite construits par seuillage global des coefficients d'ondelettes (la dependance des donnees apparait dans leur construction via une condition sommatoire) et nous montrons leurs proprietes d'adaptativite. L'idee de preuve est nouvelle et se base sur un resultat interessant de talagrand que nous generalisons aux variables melangeantes. Ce resultat fournit un controle du supremum du processus empirique sur une classe convenable de fonctions
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Dunatunga, Manimelwadu Samson 1958. "SUCCESSIVE TWO SEGMENT SEPARABLE PROGRAMMING FOR NONLINEAR MINIMAX OPTIMIZATION." Thesis, The University of Arizona, 1986. http://hdl.handle.net/10150/275509.
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Zhou, Hongbo. "A Unified Robust Minimax Framework for Regularized Learning Problems." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/dissertations/875.
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Regularization techniques have become a principled tool for model-based statistics and artificial intelligence research. However, in most situations, these regularization terms are not well interpreted, especially on how they are related to the loss function and data matrix in a given statistic model. In this work, we propose a robust minimax formulation to interpret the relationship between data and regularization terms for a large class of loss functions. We show that various regularization terms are essentially corresponding to different distortions to the original data matrix. This supplies a unified framework for understanding various existing regularization terms, designing novel regularization terms based on perturbation analysis techniques, and inspiring novel generic algorithms. To show how to apply minimax related concepts to real-world learning tasks, we develop a new fault-tolerant classification framework to combat class noise for general multi-class classification problems; further, by studying the relationship between the majorizable function class and the minimax framework, we develop an accurate, efficient, and scalable algorithm for solving a large family of learning formulations. In addition, this work has been further extended to tackle several important matrix-decomposition-related learning tasks, and we have validated our work on various real-world applications including structure-from-motion (with missing data) and latent structure dictionary learning tasks. This work, composed of a unified formulation, a scalable algorithm, and promising applications in many real-world learning problems, contributes to the understanding of various hidden robustness in many learning models. As we show, many classical statistical machine learning models can be unified using this formulation and accurate, efficient, and scalable algorithms become available from our research.
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Bateni, Amir-Hossein. "Contributions to robust estimation : minimax optimality vs. computational tractability." Electronic Thesis or Diss., Institut polytechnique de Paris, 2022. http://www.theses.fr/2022IPPAG004.
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En statistique et en théorie de l'apprentissage statistique, on suppose souvent que les échantillons sont distribués indépendamment et identiquement selon une distribution de probabilité de référence. Une approche plus réaliste pourrait consister à relaxer cette hypothèse en permettant à une fraction des échantillons de ne pas nécessairement suivre la distribution de référence. Ces échantillons désobéissants, appelés données aberrantes, peuvent considérablement détériorer la performance des estimateurs classiques. Dans ce travail, nous cherchons à estimer la moyenne des distributions de référence par des estimateurs robustes aux données aberrantes. Nous nous intéressons au comportement non-asymptotique des estimateurs. Dans un premier temps, nous décrivons divers modèles de contamination qui déterminent la nature des données aberrantes parmi nos observations. Puis, nous considérons le problème de l'estimation de la moyenne d'une distribution dont le support est le simplexe de probabilité de dimension k dans le cas où une fraction d'observations sont des données aberrantes générées par un adversaire. Un exemple particulier simple est le problème de l'estimation de la distribution d'une variable aléatoire discrète. Dans un deuxième temps, nous étudions le problème de l'estimation robuste de la moyenne d'une distribution gaussienne. Les estimateurs minimax-optimaux connus pour ce problème ne sont pas calculables en temps polynomial. Nous introduisons un estimateur efficace basé sur la réduction spectrale de dimension et établissons une borne supérieure sur son erreur qui est minimax-optimale modulo un facteur logarithmiqueIn statistics and learning theory, it is common to assume that samples are independently and identically distributed according to a reference probability distribution. A more realistic approach could be to relax this assumption by allowing a fraction of samples to not necessarily follow the reference distribution. These disobeying samples, called outliers, may drastically skew the classical estimators. In this work, we aim to estimate the mean of reference distributions by estimators robust to outliers. We are interested in the non-asymptotic behavior of the estimators. At the first stage, we describe various contamination models which determine the nature of the outliers among our observations. Then, we consider the problem of estimating the mean of a distribution supported by the k-dimensional probability simplex in the setting where an fraction of observations are outliers generated by an adversary. A simple particular example is the problem of estimating the distribution of a discrete random variable. At the second stage, we study the problem of robust estimation of the mean of a Gaussian distribution. The known minimax-optimal estimators for this problem are not computationally tractable. We introduce a computationally efficient estimator based on spectral dimension reduction and establish a finite sample upper bound on its error that is minimax-optimal up to a logarithmic factor
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Nisar, Muhammad Danish [Verfasser]. "Minimax Robustness in Signal Processing for Communications / Muhammad Danish Nisar." Aachen : Shaker, 2011. http://d-nb.info/1070152196/34.
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Wu, Zhou. "Extension theorems and minimax inequalities with applications to mathematical economics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq24767.pdf.
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Zhao, Meng. "Issues in model selection, minimax estimation, and censored data analysis." Connect to this title online, 2007. http://etd.lib.clemson.edu/documents/1202500925/.
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Slama, Bruno. "Méthode de "trust region" dans l'étude de problèmes de minimax." Clermont-Ferrand 2, 1985. http://www.theses.fr/1985CLF2A002.
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On étudie des problèmes de minimax en utilisant des méthodes de "trust région". On ne fait intervenir dans nos algorithmes que les contraintes actives à epsilon -près et on montre que ce choix est justifie par les résultats obtenus. On formule en particulier un algorithme dont la vitesse de convergence est du second ordre des lors que la solution vérifie une condition suffisante du second ordre.
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Pouet, Christophe. "Tests minimax non-paramétriques : hypothèse nulle composite et constantes exactes." Paris 6, 2000. http://www.theses.fr/2000PA066383.
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Joukovskaïa, Tatiana. "Singularités de minimax et solutions faibles d'équations aux derivées partielles." Paris 7, 1994. http://www.theses.fr/1994PA077046.
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La recherche des solutions d'une equation aux derivees partielles non lineaire sur une variete peut se faire en deux temps: on obtient d'abord des solutions geometriques, sous-varietes d'un espace de jets d'ordre approprie de fonctions reelles sur la variete ; ensuite, on regarde les projections de ces solutions geometriques dans l'espace des jets d'ordre zero (fronts d'onde, ou diagrammes de cerf). Il peut arriver que l'on cherche une vraie fonction reelle alors que le diagramme de cerf obtenu est le graphe d'une fonction multiforme ; m. Chaperon a remarque que, si l'equation est du premier ordre, il est souvent possible de construire une section de ce diagramme de cerf qui est une vraie fonction lipschitzienne, solution faible globale de l'equation. Cette solution etant construite comme minimax d'une famille generatrice quadratique a l'infini, l'etude des disontinuites (chocs) de sa differentielle est un probleme de theorie des singularites, qui fait l'objet de cette these. Apres des rappels sur les deformations verselles (1), le 2 contient le principal resultat theorique (theoreme 2. 11), etablissant en particulier que les singularites de ces fonctions minimax sont en general, a diffeomorphisme local pres, semi-algebriques ; son corollaire 2. 12 permet, dans le 3, de classifier ces singularites generiques en dimension au plus trois (theoreme 3. 1) ; lorsque cet espace de dimension trois est un espace-temps, le 4 etudie l'evolution generique des sections a temps constant du minimax. Toute cette premiere partie est concentree sur le probleme de theorie des singularites ; les applications aux equations aux derivees partielles figurent dans la seconde partie, qui contient par ailleurs des resultats nouveaux comme le theoreme 7. 1 et le contre-exemple 6. 3
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Rehmert, Ian Jon. "A Performance Analysis of the Minimax Multivariate Quality Control Chart." Thesis, Virginia Tech, 1997. http://hdl.handle.net/10919/35747.
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A performance analysis of three different Minimax control
charts is performed with respect to their Chi-Square control
chart counterparts under several different conditions. A
unique control chart must be constructed for each process
described by a unique combination of quality characteristic
mean vector and associated covariance matrix. The three
different charts under consideration differ in the number of
quality characteristic variables of concern. In each case,
without loss of generality the in-control quality
characteristic mean vector is assumed to have zero entries
and the associated covariance matrix is assumed to have
non-negative entries. The performance of the Chi-Square and
Minimax charts are compared under different values of the
sample size, the probability of a Type I error, and selected
shifts in the quality characteristic mean vector. Minimax
and Chi-Square charts that are compared share identical
in-control average run lengths (ARL) making the
out-of-control ARL the appropriate performance measure. A
combined Tausworthe pseudorandom number generator is used to
generate the out-of-control mean vectors. Issues regarding
multivariate uniform pseudorandom number generation are
addressed.Master of Science
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Slama, Bruno. "Méthodes de " Trust région " dans l'étude de problèmes de minimax." 63-Aubière : Impr. U.E.R. Sci, 1985. http://catalogue.bnf.fr/ark:/12148/cb36110330b.
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Zgheib, Rania. "Tests non paramétriques minimax pour de grandes matrices de covariance." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1078/document.
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Ces travaux contribuent à la théorie des tests non paramétriques minimax dans le modèle de grandes matrices de covariance. Plus précisément, nous observons $n$ vecteurs indépendants, de dimension $p$, $X_1,ldots, X_n$, ayant la même loi gaussienne $mathcal {N}_p(0, Sigma)$, où $Sigma$ est la matrice de covariance inconnue. Nous testons l'hypothèse nulle $H_0:Sigma = I$, où $I$ est la matrice identité. L'hypothèse alternative est constituée d'un ellipsoïde avec une boule de rayon $varphi$ autour de $I$ enlevée. Asymptotiquement, $n$ et $p$ tendent vers l'infini. La théorie minimax des tests, les autres approches considérées pour le modèle de matrice de covariance, ainsi que le résumé de nos résultats font l'objet de l'introduction.Le deuxième chapitre est consacré aux matrices de covariance $Sigma$ de Toeplitz. Le lien avec le modèle de densité spectrale est discuté. Nous considérons deux types d'ellipsoïdes, décrits par des pondérations polynomiales (dits de type Sobolev) et exponentielles, respectivement.Dans les deux cas, nous trouvons les vitesses de séparation minimax. Nous établissons également des équivalents asymptotiques exacts de l'erreur minimax de deuxième espèce et de l'erreur minimax totale. La procédure de test asymptotiquement minimax exacte est basée sur une U-statistique d'ordre 2 pondérée de façon optimale.Le troisième chapitre considère une hypothèse alternative de matrices de covariance pas nécessairement de Toeplitz, appartenant à un ellipsoïde de type Sobolev de paramètre $alpha$. Nous donnons des équivalents asymptotiques exacts des erreurs minimax de 2ème espèce et totale. Nous proposons une procédure de test adaptative, c-à-d libre de $alpha$, quand $alpha$ appartient à un compact de $(1/2, + infty)$.L'implémentation numérique des procédures introduites dans les deux premiers chapitres montrent qu'elles se comportent très bien pour de grandes valeurs de $p$, en particulier elles gagnent beaucoup sur les méthodes existantes quand $p$ est grand et $n$ petit.Le quatrième chapitre se consacre aux tests adaptatifs dans un modèle de covariance où les observations sont incomplètes. En effet, chaque coordonnée du vecteur est manquante de manière indépendante avec probabilité $1-a$, $ ain (0,1)$, où $a$ peut tendre vers 0. Nous traitons ce problème comme un problème inverse. Nous établissons ici les vitesses minimax de séparation et introduisons de nouvelles procédures adaptatives de test. Les statistiques de test définies ici ont des poids constants. Nous considérons les deux cas: matrices de Toeplitz ou pas, appartenant aux ellipsoïdes de type SobolevOur work contributes to the theory of non-parametric minimax tests for high dimensional covariance matrices. More precisely, we observe $n$ independent, identically distributed vectors of dimension $p$, $X_1,ldots, X_n$ having Gaussian distribution $mathcal{N}_p(0,Sigma)$, where $Sigma$ is the unknown covariance matrix. We test the null hypothesis $H_0 : Sigma =I$, where $I$ is the identity matrix. The alternative hypothesis is given by an ellipsoid from which a ball of radius $varphi$ centered in $I$ is removed. Asymptotically, $n$ and $p$ tend to infinity. The minimax test theory, other approaches considered for testing covariance matrices and a summary of our results are given in the introduction.The second chapter is devoted to the case of Toeplitz covariance matrices $Sigma$. The connection with the spectral density model is discussed. We consider two types of ellipsoids, describe by polynomial weights and exponential weights, respectively. We find the minimax separation rate in both cases. We establish the sharp asymptotic equivalents of the minimax type II error probability and the minimax total error probability. The asymptotically minimax test procedure is a U-statistic of order 2 weighted by an optimal way.The third chapter considers alternative hypothesis containing covariance matrices not necessarily Toeplitz, that belong to an ellipsoid of parameter $alpha$. We obtain the minimax separation rate and give sharp asymptotic equivalents of the minimax type II error probability and the minimax total error probability. We propose an adaptive test procedure free of $alpha$, for $alpha$ belonging to a compact of $(1/2, + infty)$.We implement the tests procedures given in the previous two chapters. The results show their good behavior for large values of $p$ and that, in particular, they gain significantly over existing methods for large $p$ and small $n$.The fourth chapter is dedicated to adaptive tests in the model of covariance matrices where the observations are incomplete. That is, each value of the observed vector is missing with probability $1-a$, $a in (0,1)$ and $a$ may tend to 0. We treat this problem as an inverse problem. We establish the minimax separation rates and introduce new adaptive test procedures. Here, the tests statistics are weighted by constant weights. We consider ellipsoids of Sobolev type, for both cases : Toeplitz and non Toeplitz matrices
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Capitanio, Gianmarco. "Familles Tangentielles et solutions de minimax pour l'équation de Hamilton-Jacobi." Phd thesis, Université Paris-Diderot - Paris VII, 2004. http://tel.archives-ouvertes.fr/tel-00008669.
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Cette Thèse porte sur les familles tangentielles et les équations de Hamilton--Jacobi. Ces deux sujets sont reliés à des thèmes classiques en théorie des singularités, comme la théorie des enveloppes, les singularités des fronts d'onde et des caustiques, la géométrie symplectique et de contact.
Les premiers trois chapitres de la Thèse sont consacrés à l'étude des familles tangentielles, à la classification de leurs singularités stables et simples, et à leurs interprétation dans le cadre de la Géométrie de Contact.
Le dernier chapitre est dédié à l'étude des solutions de minimax pour l'équation de Hamilton--Jacobi, notamment à la classification des leurs singularités génériques de petite codimension.
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Nutini, Julie Ann. "A derivative-free approximate gradient sampling algorithm for finite minimax problems." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42200.
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Mathematical optimization is the process of minimizing (or maximizing) a function. An algorithm is used to optimize a function when the minimum cannot be found by hand, or finding the minimum by hand is inefficient. The minimum of a function is a critical point and corresponds to a gradient (derivative) of 0. Thus, optimization algorithms commonly require gradient calculations. When gradient information of the objective function is unavailable, unreliable or ‘expensive’ in terms of computation time, a derivative-free optimization algorithm is ideal. As the name suggests, derivative-free optimization algorithms do not require gradient calculations. In this thesis, we present a derivative-free optimization algorithm for finite minimax problems. Structurally, a finite minimax problem minimizes the maximum taken over a finite set of functions. We focus on the finite minimax problem due to its frequent appearance in real-world applications. We present convergence results for a regular and a robust version of our algorithm, showing in both cases that either the function is unbounded below (the minimum is −∞) or we have found a critical point. Theoretical results are explored for stopping conditions. Additionally, theoretical and numerical results are presented for three examples of approximate gradients that can be used in our algorithm: the simplex gradient, the centered simplex gradient and the Gupal estimate of the gradient of the Steklov averaged function. A performance comparison is made between the regular and robust algorithm, the three approximate gradients, and the regular and robust stopping conditions. Finally, an application in seismic retrofitting is discussed.
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D'Silva, Karl. "Two Approaches to the Isotonic Change-Point Problem: Nonparametric and Minimax." Diss., North Dakota State University, 2014. https://hdl.handle.net/10365/27402.
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A change in model parameters over time often characterizes major events. Situations in which this may arise include observing increasing temperatures, intense rainfall, and the valuation of a stock. The question is whether these observations are simply the result of natural variation, or rather are indicative of an underlying monotonic trend. This is known as the isotonic change-point problem. Two approaches to this problem are considered: Firstly, for correlated data with short-range dependence, we prove that a particular U-statistic based on a modified version of the Jonckheere-Terpstra test statistic is asymptotically equivalent to a more complex U-statistic discussed by Shen and Xu (2013); one that has been shown to outperform other existing tests in a variety of situations. Secondly, we shall justify and utilize the minimax criterion in order to identify the optimal test statistic within a specified class. We shall see that, as motivated by the projection method, the aforementioned class is the class of contrasts. It shall be proven that the set of coefficients originally proposed by Abelson and Tukey (1963), and utilized by Brillinger (1989) in the isotonic change-point setting, are in fact minimax in the independent data case. For correlated data with shortrange dependence, we shall demonstrate a sufficient condition for minimaxity to hold.
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Gutzeit, Maurilio [Verfasser], and Alexandra [Gutachter] Carpentier. "Topics in statistical minimax hypothesis testing / Maurilio Gutzeit ; Gutachter: Alexandra Carpentier." Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2019. http://d-nb.info/1220036242/34.
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Clémençon, Stéphan. "Méthodes d'ondelettes pour la statistique non paramétrique des chaînes de Markov." Paris 7, 2000. http://www.theses.fr/2000PA077042.
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Zhang, Hui [Verfasser]. "Relativistic LCAO with Minimax Principle and New Balanced Basis Sets / Hui Zhang." Kassel : Universitätsbibliothek Kassel, 2011. http://d-nb.info/1009770349/34.
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Schluttenhofer, Sandra [Verfasser], and Jan [Akademischer Betreuer] Johannes. "Adaptive Minimax Testing for Inverse Problems / Sandra Simone Schluttenhofer ; Betreuer: Jan Johannes." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1225484464/34.
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Dharmakadar, Aida. "An algorithmic solution to the minimax resource allocation problem with multimodal functions." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-10062009-020310/.
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Schluttenhofer, Sandra Simone [Verfasser], and Jan [Akademischer Betreuer] Johannes. "Adaptive Minimax Testing for Inverse Problems / Sandra Simone Schluttenhofer ; Betreuer: Jan Johannes." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1225484464/34.
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Hütter, Jan-Christian Klaus. "Minimax estimation with structured data : shape constraints, causal models, and optimal transport." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122184.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019Cataloged from PDF version of thesis.
Includes bibliographical references (pages 275-299).
Modern statistics often deals with high-dimensional problems that suffer from poor performance guarantees and from the curse of dimensionality. In this thesis, we study how structural assumptions can be used to overcome these difficulties in several estimation problems, spanning three different areas of statistics: shape-constrained estimation, causal discovery, and optimal transport. In the area of shape-constrained estimation, we study the estimation of matrices, first under the assumption of bounded total-variation (TV) and second under the assumption that the underlying matrix is Monge, or supermodular. While the first problem has a long history in image denoising, the latter structure has so far been mainly investigated in the context of computer science and optimization. For TV denoising, we provide fast rates that are adaptive to the underlying edge sparsity of the image, as well as generalizations to other graph structures, including higher-dimensional grid-graphs. For the estimation of Monge matrices, we give near minimax rates for their estimation, including the case where latent permutations act on the rows and columns of the matrix. In the latter case, we also give two computationally efficient and consistent estimators. Moreover, we show how to obtain estimation rates in the related problem of estimating continuous totally positive distributions in 2D. In the area of causal discovery, we investigate a linear cyclic causal model and give an estimator that is near minimax optimal for causal graphs of bounded in-degree. In the area of optimal transport, we introduce the notion of the transport rank of a coupling and provide empirical and theoretical evidence that it can be used to significantly improve rates of estimation of Wasserstein distances and optimal transport plans. Finally, we give near minimax optimal rates for the estimation of smooth optimal transport maps based on a wavelet regularization of the semi-dual objective.
by Jan-Christian Klaus Hütter.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
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Royer, Martin. "Optimalité statistique du partitionnement par l'optimisation convexe." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS442/document.
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Ces travaux traitent de la problématique du partitionnement d'un ensemble d'observations ou de variables en groupes d'éléments similaires. Elle sert de nombreuses applications essentielles comme la classification de gènes en biologie ou l'apprentissage automatique en analyse d'image. Les travaux modélisent la notion de similarité entre éléments pour analyser les propriétés statistiques d'algorithmes de partitionnement, comme l'estimateur des K-moyennes. Ce dernier est équivalent au maximum de vraisemblance quand les groupes considérés sont homoscedastiques ; dans le cas contraire, on s'aperçoit que l'estimateur est biaisé, en ce qu'il tend à séparer les groupes ayant une plus grande dispersion. En utilisant une formulation équivalente qui fait intervenir l'optimisation semi-définie positive, on propose une correction opérationnelle de ce biais. On construit et étudie ainsi des algorithmes de complexité polynomiale qui sont quasi-minimax pour le partitionnement exact dans les deux contextes étudiés. Ces résultats s'interprètent dans le cadre de modèles standards comme le modèle de mélange ou le modèle à variables latentes, et s'étendent à de nouveaux modèles plus généraux et plus robustes, les modèles $G$-block. Les contrôles peuvent être adaptés au nombre intrinsèque de groupes, ainsi qu'à la dimension effective de l'espace des données. Ils apportent une meilleure compréhension d'estimateurs classiques du partitionnement comme les estimateurs spectraux. Ils sont appuyés par des expériences extensives sur données de synthèse, ainsi que sur des jeux de données réelles. Enfin lorsqu'on cherche à améliorer l'efficacité computationnelle des algorithmes étudiés, on peut utiliser une connexion forte avec le domaine de l'optimisation convexe et notamment exploiter des techniques de relaxation de faible rang motivées par des problématiques de grande dimensionThis work focuses on the problem of point and variable clustering, that is the grouping of either similar vectors or similar components of a vector in a metric space. This has applications in many relevant fields including pattern recognition in image analysis or gene expression data classification. Through adequate modeling of the similarity between points or variables within a cluster we analyse the statistical properties of known clustering algorithms such as K-means.When considering homoscedastic elements for all groups the K-means algorithm is equivalent to a maximum-likelihood procedure. Otherwise the algorithm shows bias in the sense that it tends to separate groups with larger dispersion, regardless of actual group separation. By using a semi definite positive reformulation of the estimator, we suggest a pattern of correction for the algorithm that leads to the construction of computational algorithm with quasiminimax properties for hard clustering of points or variables.Those results can be studied under the classical mixture model or latent variables model, and can be extended to more general and robust class of $G$-block models. The stochastic controls can be made adaptive to the unknown number of classes as well as to the effective dimension of the problem. They help understand the behavior of the class of spectral estimators that are also widely used for clustering problems. They are supported by extensive simulation studies as well as data analysis stemming from the biological field.When focus is brought on the computational aspect of those algorithms, we exploit ideas based on a strong connexion with the domain of convex optimisation and specifically the technique of low-rank relaxation, of importance when dealing with high dimensional problems
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Jeanjean, Louis. "Approche minimax des solutions d'une équation semi-linéaire elliptique en l'absence de compacité /." [S.l.] : [s.n.], 1992. http://library.epfl.ch/theses/?nr=1041.
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Gayraud, Ghislaine. "Vitesses et procédures statistiques minimax dans des problèmes d'estimation et des tests d'hypothèses." Habilitation à diriger des recherches, Université de Rouen, 2007. http://tel.archives-ouvertes.fr/tel-00207687.
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Mes travaux s'articulent autour de trois thématiques. La première thèmatique porte sur la résolution via l'approche minimax de divers problèmes d'estimation et de tests d'hypothèses dans un cadre non-paramétrique.
En statistique Bayésienne non-paramétrique, je me suis intéressée à un problème d'estimation d'ensembles à niveau. Les résultats obtenus résultent de l'étude des propriétés asymptotiques d'estimation Bayésienne d'ensembles à niveau. Ce sont des résultats généraux au sens où la consistance et la vitesse de convergence de l'estimateur Bayésien sont établies pour une large classe de lois a priori.
La troisième thématique concerne un problème d'estimation paramétrique dans un modèle de déconvolution aveugle bruitée : il s'agit de restituer la loi du signal entrant. La consistance ainsi que la distribution asymptotique d'une nouvelle procédure d'estimation sont établies.
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Pee, Eng Yau. "On algorithms for nonlinear minimax and min-max-min problems and their efficiency." Monterey, California. Naval Postgraduate School, 2011. http://hdl.handle.net/10945/10782.
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This dissertation approaches the solution of optimization models with uncertain parameters by considering the worst-case value of the uncertain parameters during optimization. We consider three problems resulting from this approach: a finite minimax problem (FMX), a semi-infinite minimax problem (SMX), and a semi-infinite minmax-min problem (MXM). In all problems, we consider nonlinear functions with continuous variables. We find that smoothing algorithms for (FMX) may only have sublinear rates of convergence, but their complexity in the number of functions is competitive with other algorithms. We present two new smoothing algorithms with novel precision-adjustment schemes for (FMX). For (SMX) algorithms, we present a novel way of expressing rate of convergence in terms of computational work instead of the typical number of iterations, and show how the new way allows for a fairer comparison of different algorithms. We propose a new approach to solve (MXM), based on discretization and reformulation of (MXM) as a constrained finite minimax problem. Our approach is the first to solve (MXM) in the general case where the innermost feasible region depends on the variables in the outer problems. We conduct numerical studies for all three problems.
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Iwamura, Rafael Santos. "Minimax approach applied to topology optimization of structures subjected to multiple load cases." Instituto Tecnológico de Aeronáutica, 2013. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2834.
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This work investigates a topology optimization strategy for structures under multiple load cases. Typically compliance is calculated for each of the load cases in analysis and minimization is computed for a weighted average of the compliances, resulting in time consuming algorithms. A way to increase convergence speed is updating density on the element level. Instead of having an averaged compliance for the whole structure, it is proposed to compute it individually for every element. All load cases are analyzed, however only the ones of the maximum compliances are considered for sensitivity analysis. Thus compliance gradient is function of a few load cases at each element, reducing the processing time without significant weight penalty. The efficiency of the proposed technique is exemplified and compared to the one of a classical approach of multiple load case problem, solved using optimality criteria.
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Foksová, Eva. "Jsou tenisté racionální?" Master's thesis, Vysoká škola ekonomická v Praze, 2011. http://www.nusl.cz/ntk/nusl-114452.
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The aim of this thesis is to verify the hypothesis on real data based on economic theory and these theories to confirm or reject. The first part deals with testing of hypotheses based on the game theory and tests whether tennis players play according to the minimax theory. The Hypotheses analyse the data for strong and weak players, considering their service, and verify which group of players converge in their strategies toward minimax theory assumptions. Specifically, theory components of the hypotheses are tested within this part: i) the probability of winning the game serving from the right side of a court is the same as the probability of winning the game serving from the left side, ii) this hypothesis will hold true rather in case of stronger players serving against weaker players than in case equally strong players playing against each other and iii) Based on the assumption that women do not excel distinctively in serving, the results in the women's matches will be worse in the minimax theory than results from men's matches. Hypotheses derived from the theory of elimination tournaments are tested in the second part of the diploma thesis. The hypotheses are analysed on the tennis data whether players make less effort in uneven tournaments, regardless of their position as favourite or outsider, than the theory presumes. The analysis of the above mentioned hypotheses was performed on the data from the Grand Slam tournaments in the years 2011 and 2012. Hypotheses are tested using both male and female data. The results obtained from analysis of the data confirm the hypotheses.
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Yao, Xudong. "Minimax methods for finding multiple saddle critical points in Banach spaces and their applications." Diss., Texas A&M University, 2004. http://hdl.handle.net/1969.1/2732.
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This dissertation was to study computational theory and methods for ?nding multiple saddle critical points in Banach spaces. Two local minimax methods were developed for this purpose. One was for unconstrained cases and the other was for constrained cases. First, two local minmax characterization of saddle critical points in Banach spaces were established. Based on these two local minmax characterizations, two local minimax algorithms were designed. Their ?ow charts were presented. Then convergence analysis of the algorithms were carried out. Under certain assumptions, a subsequence convergence and a point-to-set convergence were obtained. Furthermore, a relation between the convergence rates of the functional value sequence and corresponding gradient sequence was derived. Techniques to implement the algorithms were discussed. In numerical experiments, those techniques have been successfully implemented to solve for multiple solutions of several quasilinear elliptic boundary value problems and multiple eigenpairs of the well known nonlinear p-Laplacian operator. Numerical solutions were presented by their pro?les for visualization. Several interesting phenomena of the solutions of quasilinear elliptic boundary value problems and the eigenpairs of the p-Laplacian operator have been observed and are open for further investigation. As a generalization of the above results, nonsmooth critical points were considered for locally Lipschitz continuous functionals. A local minmax characterization of nonsmooth saddle critical points was also established. To establish its version in Banach spaces, a new notion, pseudo-generalized-gradient has to be introduced. Based on the characterization, a local minimax algorithm for ?nding multiple nonsmooth saddle critical points was proposed for further study.
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Howe, Melendres Amoro. "A quasi-Newton algorithm for continuous minimax with applications to risk management in finance." Thesis, Imperial College London, 1994. http://hdl.handle.net/10044/1/11772.
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Babenko, V. A. "Dynamical models of the minimax program management of innovation processes in interprises with risks." Thesis, NTU "KhPI", 2016. http://repository.kpi.kharkov.ua/handle/KhPI-Press/26209.
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