Dissertations / Theses on the topic 'Least squares'
To see the other types of publications on this topic, follow the link: Least squares.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Least squares.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Jones, Caroline Erin. "Least squares Gaussian quadrature." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0017/MQ54628.pdf.
Full text
2
Hassel, Per Anker. "Nonlinear partial least squares." Thesis, University of Newcastle Upon Tyne, 2003. http://hdl.handle.net/10443/465.
Full textAbstract:
Partial Least Squares (PLS) has been shown to be a versatile regression technique with an increasing number of applications in the areas of process control, process monitoring and process analysis. This Thesis considers the area of nonlinear PLS; a nonlinear projection based regression technique. The nonlinearity is introduced as a univariate nonlinear function between projections, or to be more specific, linear combinations of the predictor and the response variables. As for the linear case, the method should handle multicollinearity, underdetermined and noisy systems. Although linear PLS is accepted as an empirical regression method, none of the published nonlinear PLS algorithms have achieved widespread acceptance. This is confirmed from a literature survey where few real applications of the methodology were found. This Thesis investigates two nonlinear PLS methodologies, in particular focusing on their limitations. Based on these studies, two nonlinear PLS algorithms are proposed. In the first of the two existing approaches investigated, the projections are updated by applying an optimization method to reduce the error of the nonlinear inner mapping. This ensures that the error introduced by the nonlinear inner mapping is minimized. However, the procedure is limited as a consequence of problems with the nonlinear optimisation. A new algorithm, Nested PLS (NPLS), is developed to address these issues. In particular, a separate inner PLS is used to update the projections. The NPLS algorithm is shown to outperform existing algorithms for a wide range of regression problems and has the potential to become a more widely accepted nonlinear PLS algorithm than those currently reported in the literature. In the second of the existing approaches, the projections are identified by examining each variable independently, as opposed to minimizing the error of the nonlinear inner mapping directly. Although the approach does not necessary identify the underlying functional relationship, the problems of overfitting and other problems associated with optimization are reduced. Since the underlying functional relationship may not be established accurately, the reliability of the nonlinear inner mapping will be reduced. To address this problem a new algorithm, the Reciprocal Variance PLS (RVPLS), is proposed. Compared with established methodology, RVPLS focus more on finding the underlying structure, thus reducing the difficulty of finding an appropriate inner mapping. RVPLS is shown to perform well for a number of applications, but does not have the wide-ranging performance of Nested PLS.
3
Ganssle, Graham. "Stabilized Least Squares Migration." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2074.
Full textAbstract:
Before raw seismic data records are interpretable by geologists, geophysicists must process these data using a technique called migration. Migration spatially repositions the acoustic energy in a seismic record to its correct location in the subsurface. Traditional migration techniques used a transpose approximation to a true acoustic propagation operator. Conventional least squares migration uses a true inverse operator, but is limited in functionality by the large size of modern seismic datasets. This research uses a new technique, called stabilized least squares migration, to correctly migrate seismic data records using a true inverse operator. Contrary to conventional least squares migration, this new technique allows for errors over ten percent in the underlying subsurface velocity model, which is a large limitation in conventional least squares migration. The stabilized least squares migration also decreases the number of iterations required by conventional least squares migration algorithms by an average of about three iterations on the sample data tested in this research.
4
Young, William Ronald. "Total least squares and constrained least squares applied to frequency domain system identification." Ohio : Ohio University, 1993. http://www.ohiolink.edu/etd/view.cgi?ohiou1176315127.
Full text
5
Guo, Hengdao. "Frequency Tracking and Phasor Estimation Using Least Squares and Total Least Squares Algorithms." UKnowledge, 2014. http://uknowledge.uky.edu/ece_etds/57.
Full textAbstract:
System stability plays an important role in electric power systems. With the development of electric power system, the scale of the electric grid is now becoming larger and larger, and many renewable energy resources are integrated in the grid. However, at the same time, the stability and safety issues of electric power system are becoming more complicated. Frequency and phasors are two critical parameters of the system stability. Obtaining these two parameters have been great challenges for decades. Researchers have provided various kinds of algorithms for frequency tracking and phasor estimation. Among them, Least Squares (LS) algorithm is one of the most commonly used algorithm. This thesis studies the LS algorithm and the Total Least Squares (TLS) algorithm working on frequency tracking and phasor estimation. In order to test the performance of the two algorithms, some simulations have been made in the Matlab. The Total Vector Error (TVE) is a commonly used performance criteria, and the TVE results of the two algorithms are compared. The TLS algorithm performs better than LS algorithm when the frequencies of all harmonic components are given.
6
Santiago, Claudio Prata. "On the nonnegative least squares." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31768.
Full textAbstract:
Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.Committee Chair: Earl Barnes; Committee Member: Arkadi Nemirovski; Committee Member: Faiz Al-Khayyal; Committee Member: Guillermo H. Goldsztein; Committee Member: Joel Sokol. Part of the SMARTech Electronic Thesis and Dissertation Collection.
7
Müller, Werner. "On Least Squares Variogram Fitting." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1997. http://epub.wu.ac.at/370/1/document.pdf.
Full text
8
Yao, Gang. "Least-squares reverse-time migration." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/14575.
Full textAbstract:
Conventional migration methods, including reverse-time migration (RTM) have two weaknesses: first, they use the adjoint of forward-modelling operators, and second, they usually apply a crosscorrelation imaging condition to extract images from reconstructed wavefields. Adjoint operators, which are an approximation to inverse operators, can only correctly calculate traveltimes (phase), but not amplitudes. To preserve the true amplitudes of migration images, it is necessary to apply the inverse of the forward-modelling operator. Similarly, crosscorrelation imaging conditions also only correct traveltimes (phase) but do not preserve amplitudes. Besides, the examples show crosscorrelation imaging conditions produce strong sidelobes. Least-squares migration (LSM) uses both inverse operators and deconvolution imaging conditions. As a result, LSM resolves both problems in conventional migration methods and produces images with fewer artefacts, higher resolution and more accurate amplitudes. At the same time, RTM can accurately handle all dips, frequencies and any type of velocity variation. Combining RTM and LSM produces least-squares reverse-time migration (LSRTM), which in turn has all the advantages of RTM and LSM. In this thesis, we implement two types of LSRTM: matrix-based LSRTM (MLSRTM) and non-linear LSRTM (NLLSRTM). MLSRTM is a matrix formulation of LSRTM and is more stable than conventional LSRTM; it can be implemented with linear inversion algorithms but needs a large amount of computer memory. NLLSRTM, by contrast, directly expresses migration as an optimisation which minimises the 2 norm of the residual between the predicted and observed data. NLLSRTM can be implemented using non-linear gradient inversion algorithms, such as non-linear steepest descent and non-linear conjugated-gradient solvers. We demonstrate that both MLSRTM and NLLSRTM can achieve better images with fewer artefacts, higher resolution and more accurate amplitudes than RTM using three synthetic examples. The power of LSRTM is also further illustrated using a field dataset. Finally, a simple synthetic test demonstrates that the objective function used in LSRTM is sensitive to errors in the migration velocity. As a result, it may be possible to use NLLSRTM to both refine the migrated image and estimate the migration velocity.
9
Kim, Donggeon. "Least squares mixture decomposition estimation." Diss., This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-02132009-171622/.
Full text
10
Chu, Ka Lok 1975. "Inequalities and equalities associated with ordinary least squares and generalized least squares in partitioned linear models." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85140.
Full textAbstract:
The motivation for this thesis is the paper by Paul L. Canner [The American Statistician, vol. 23, no. 5, pp. 39--40 (1969)] in which it was noted that in simple linear regression it is possible for the generalized least squares regression line to lie either entirely above or entirely below all of the observed data points.Chapter I builds on the observation that in Canner's model the ordinary least squares and generalized least squares regression lines are parallel, which led us to introduce a new measure of efficiency of ordinary least squares and to find conditions for which the total Watson efficiency of ordinary least squares in a partitioned linear model exceeds or is less than the product of the two subset Watson efficiencies, i.e., the product of the Watson efficiencies associated with the two subsets of parameters in the underlying partitioned linear model.
We introduce the notions of generalized efficiency function, efficiency factorization multiplier, and determinantal covariance ratio, and obtain several inequalities and equalities. We give special attention to those partitioned linear models for which the total Watson efficiency of ordinary least squares equals the product of the two subset Watson efficiencies. A key characterization involves the equality between the squares of a certain partial correlation coefficient and its associated ordinary correlation coefficient.
In Chapters II and IV we suppose that the underlying partitioned linear model is weakly singular in that the column space of the model matrix is contained in the column space of the covariance matrix of the errors in the linear model. In Chapter III our results are specialized to partitioned linear models where the partitioning is orthogonal and the covariance matrix of the errors is positive definite.
11
Kubitz, Jörg. "Gemischte Least-Squares-FEM für Elastoplastizität." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=983832625.
Full text
12
Kolev, Tzanio Valentinov. "Least-squares methods for computational electromagnetics." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1115.
Full textAbstract:
The modeling of electromagnetic phenomena described by the Maxwell's equations is of critical importance in many practical
applications. The numerical simulation of these equations is challenging and much more involved than initially believed. Consequently, many discretization techniques, most of them quite complicated, have been proposed.
In this dissertation, we present and analyze a new methodology for approximation of the time-harmonic Maxwell's equations. It is an extension of the negative-norm least-squares finite element approach which has been applied successfully to a variety of other problems.
The main advantages of our method are that it uses simple, piecewise polynomial, finite element spaces, while giving quasi-optimal approximation, even for solutions with low
regularity (such as the ones found in practical applications). The numerical solution can be efficiently computed using standard and well-known tools, such as iterative methods
and eigensolvers for symmetric and positive definite
systems (e.g. PCG and LOBPCG) and reconditioners for second-order problems (e.g. Multigrid).
Additionally, approximation of varying polynomial degrees is allowed and spurious eigenmodes are provably avoided.
We consider the following problems related to the Maxwell's equations in the frequency domain: the magnetostatic problem, the electrostatic problem, the eigenvalue problem and the full time-harmonic system. For each of these problems, we present a natural (very) weak
variational formulation assuming minimal regularity of the solution. In each case, we prove error estimates for the approximation
with two different discrete least-squares methods. We also show how to deal with problems posed on domains that are multiply connected or have multiple boundary components.
Besides the theoretical analysis of the methods, the dissertation provides various numerical results in two and three dimensions
that illustrate and support the theory.
13
Baykal, Buyurman. "Underdetermined recursive least-squares adaptive filtering." Thesis, Imperial College London, 1995. http://hdl.handle.net/10044/1/7790.
Full text
14
Fraley, Christina. "Solution of nonlinear least-squares problems /." Stanford, CA : Dept. of Computer Science, Stanford University, 1987. http://doi.library.cmu.edu/10.1184/OCLC/19613955.
Full textAbstract:
Thesis (Ph. D.)--Stanford University, 1987."June 1987." This research was supported in part by Joseph Oliger under Office of Naval Research contract N00014-82-K-0335, by Stanford Linear Accelerator Center and the Systems Optimization Laboratory under Army Research Office contract DAAG29-84-K-0156. Includes bibliographies.
15
Silva, Aristeguieta Maria. "Optimization of seismic least-squares inversion /." Access abstract and link to full text, 1993. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9325432.
Full text
16
Han, Qing 1980. "Solving constrained integer least squares problems." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98720.
Full textAbstract:
The objective of this thesis is to design efficient algorithms for solving constrained integer least squares (ILS) problems. These problems may arise from many applications, such as communications and cryptography. In this thesis, we mainly consider two kinds of constrained ILS problems: box-constrained integer least squares (BILS) problem and ellipsoid-constrained integer least squares (EILS) problem.Solving a constrained ILS problem usually has two stages: reduction (or preprocessing) and search. We first present a reduction algorithm and a search algorithm for solving the BILS problem. Unlike the usual reduction algorithms, which use only the information of the generator matrix, the new reduction algorithm also uses the information of the given input vector and the box constraint. The new search algorithm overcomes some shortcomings of the existing search algorithms and gives some other improvements. Then, for solving the EILS problem, we dynamically transfer it to a BILS problem and extend the above new search algorithm. In addition, we suggest using the well-known LLL reduction for preprocessing. For both problems, simulation results indicate the combination of our reduction algorithms and search algorithms can be (much) more efficient than the existing algorithms.
17
Hawes, Anthony H. "Least squares and adaptive multirate filtering." Thesis, Monterey, California. Naval Postgraduate School, 2012.
Find full textAbstract:
Approved for public release; distribution in unlimited.This thesis addresses the problem of estimating a random process from two observed signals sampled at different rates. The case where the low-rate observation has a higher signal-to- noise ratio than the high-rate observation is addressed. Both adaptive and non-adaptive filtering techniques are explored. For the non-adaptive case, a multirate version of the Wiener-Hopf optimal filter is used for estimation. Three forms of the filter are described. It is shown that using both observations with this filter achieves a lower mean-squared error than using either sequence alone. Furthermore, the amount of training data to solve for the filter weights is comparable to that needed when using either sequence alone. For the adaptive case, a multirate version of the LMS adaptive algorithm is developed. Both narrowband and broadband interference are removed using the algorithm in an adaptive noise cancellation scheme. The ability to remove interference at the high rate using observations taken at the low rate without the high-rate observations is demonstrated.
18
RENTERIA, RAUL PIERRE. "ALGORITHMS FOR PARTIAL LEAST SQUARES REGRESSION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4362@1.
Full textAbstract:
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOMuitos problemas da área de aprendizagem automática tem por objetivo modelar a complexa relação existente num sisitema , entre variáveis de entrada X e de saída Y na ausência de um modelo teórico. A regressão por mínimos quadrados parciais PLS ( Partial Least Squares) constitui um método linear para resolução deste tipo de problema , voltado para o caso de um grande número de variáveis de entrada quando comparado com número de amostras. Nesta tese , apresentamos uma variante do algoritmo clássico PLS para o tratamento de grandes conjuntos de dados , mantendo um bom poder preditivo. Dentre os principais resultados destacamos um versão paralela PPLS (Parallel PLS ) exata para o caso de apenas um variável de saída e um versão rápida e aproximada DPLS (DIRECT PLS) para o caso de mais de uma variável de saída. Por outro lado ,apresentamos também variantes para o aumento da qualidade de predição graças à formulação não linear. São elas o LPLS ( Lifted PLS ), algoritmo para o caso de apenas uma variável de saída, baseado na teoria de funções de núcleo ( kernel functions ), uma formulação kernel para o DPLS e um algoritmo multi-kernel MKPLS capaz de uma modelagemmais compacta e maior poder preditivo, graças ao uso de vários núcleos na geração do modelo.
The purpose of many problems in the machine learning field isto model the complex relationship in a system between the input X and output Y variables when no theoretical model is available. The Partial Least Squares (PLS)is one linear method for this kind of problem, for the case of many input variables when compared to the number of samples. In this thesis we present versions of the classical PLS algorithm designed for large data sets while keeping a good predictive power. Among the main results we highlight PPLS (Parallel PLS), a parallel version for the case of only one output variable, and DPLS ( Direct PLS), a fast and approximate version, for the case fo more than one output variable. On the other hand, we also present some variants of the regression algorithm that can enhance the predictive quality based on a non -linear formulation. We indroduce LPLS (Lifted PLS), for the case of only one dependent variable based on the theory of kernel functions, KDPLS, a non-linear formulation for DPLS, and MKPLS, a multi-kernel algorithm that can result in a more compact model and a better prediction quality, thankas to the use of several kernels for the model bulding.
19
Hawes, Anthony H. "Least squares and adaptive multirate filtering /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2003. http://library.nps.navy.mil/uhtbin/hyperion-image/03sep%5FHawes.pdf.
Full textAbstract:
Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, September 2003.Thesis advisor(s): Charles W. Therrien, Roberto Cristi. Includes bibliographical references (p. 45). Also available online.
20
Hazra, Rajeeb. "Constrained least-squares digital image restoration." W&M ScholarWorks, 1995. https://scholarworks.wm.edu/etd/1539623865.
Full textAbstract:
The design of a digital image restoration filter must address four concerns: the completeness of the underlying imaging system model, the validity of the restoration metric used to derive the filter, the computational efficiency of the algorithm for computing the filter values and the ability to apply the filter in the spatial domain. Consistent with these four concerns, this dissertation presents a constrained least-squares (CLS) restoration filter for digital image restoration. The CLS restoration filter is based on a comprehensive, continuous-input/discrete- processing/continuous-output (c/d/c) imaging system model that accounts for acquisition blur, spatial sampling, additive noise and imperfect image reconstruction. The c/d/c model-based CLS restoration filter can be applied rigorously and is easier to compute than the corresponding c/d/c model-based Wiener restoration filter. The CLS restoration filter can be efficiently implemented in the spatial domain as a small convolution kernel. Simulated restorations are used to illustrate the CLS filter's performance for a range of imaging conditions. Restoration studies based, in part, on an actual Forward Looking Infrared (FLIR) imaging system, show that the CLS restoration filter can be used for effective range reduction. The CLS restoration filter is also successfully tested on blurred and noisy radiometric images of the earth's outgoing radiation field from a satellite-borne scanning radiometer used by the National Aeronautics and Space Administration (NASA) for atmospheric research.
21
Guo, Ronggang. "Systematical analysis of the transformation procedures in Baden-Württemberg with Least Squares and Total Least Squares methods." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2007. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-33293.
Full text
22
Furrer, Marc. "Numerical Accuracy of Least Squares Monte Carlo." St. Gallen, 2008. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/01650217002/$FILE/01650217002.pdf.
Full text
23
Petra, Stefania. "Semismooth least squares methods for complementarity problems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98174558X.
Full text
24
Pei, Sun. "Noise Resistant Least Squares Based Adaptive Control." Thesis, KTH, Reglerteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-92628.
Full text
25
Kong, Seunghyun. "Linear programming algorithms using least-squares method." Diss., Available online, Georgia Institute of Technology, 2007, 2007. http://etd.gatech.edu/theses/available/etd-04012007-010244/.
Full textAbstract:
Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2007.Martin Savelsbergh, Committee Member ; Joel Sokol, Committee Member ; Earl Barnes, Committee Co-Chair ; Ellis L. Johnson, Committee Chair ; Prasad Tetali, Committee Member.
26
Titley-Péloquin, David. "Backward pertubation analysis of least squares problems." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=94973.
Full textAbstract:
This thesis is concerned with backward perturbation analyses of the linear least squares (LS) and related problems. Two theoretical measures are commonly used for assessing the backward errors that arise in the approximate solution of such problems. These are called the normwise relative backward error (NRBE) and the minimal backward error (MBE). An important new relationship between these two measures is presented, which shows that the two are essentially equivalent. New upper bounds on the NRBE and MBE for the LS problem are given and related to known bounds and estimates. One important use of backward perturbation analysis is to design stopping criteria for iterative methods. In this thesis, minimum-residual iterative methods for solving LS problems are studied. Unexpected convergence behaviour in these methods is explained and applied to show that commonly used stopping criteria can in some situations be much too conservative. More reliable stopping criteria are then proposed, along with an efficient implementation in the iterative algorithm LSQR. In many applications the data in the LS problem come from a statistical linear model in which the noise follows a multivariate normal distribution whose mean is zero and whose covariance matrix is the scaled identity matrix. A description is given of typical convergence of the error that arises in minimum-residual iterative methods when the data come from such a linear model. Stopping criteria that use the information from the linear model are then proposed and compared to others that appear in the literature. Finally, some of these ideas are extended to the scaled total least squares problem.Nous effectuons une analyse de l'erreur rétrograde des problèmes de moindres carrés. Nous analysons deux méthodes habituellement utilisées pour mesurer l'erreur rétrograde et démontrons que celles-ci sont en fait équivalentes. Nous présentons de nouvelles estimations de l'erreur rétrograde des problèmes de moindres carrés, et nous les comparons aux estimations connues. L'un des usages de ce type d'analyse consiste à établir des critères d'arrêt pour les méthodes itératives. Nous expliquons des phénomènes de convergence inattendus que nous avons observés dans les méthodes itératives de type résidu minimal. Nous démontrons ensuite que les critères d'arrêt habituellement utilisés avec ces méthodes peuvent être trop prudents dans certaines circonstances. Nous proposons donc de nouveaux critères d'arrêt plus fiables, et présentons une implémentation efficace de ceux-ci dans l'algorithme LSQR. La méthode des moindres carrés est souvent utilisée en statistique lorsque les données proviennent d'un modèle linéaire et que le bruit est distribué selon une loi normale dont l'espérance est zéro et la variance est la matrice identité proportionnée. Nous décrivons la convergence de l'erreur qui résulte de ce type de données et proposons des critères d'arrêt adaptés à cette situation. Enfin, nous appliquons une partie de cette analyse aux problèmes de moindres carrés proportionnés.
27
Breen, Stephen. "Integer least squares search and reduction strategies." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=106561.
Full textAbstract:
This thesis is concerned with integer least squares problems, also referred to as closest vector problems. One often used approach to solving these problems is the discrete search method, which typically involves two stages, the reduction and the search. The main purpose of the reduction is to make the search faster. Reduction strategies for box-constrained integer least squares problems involve column reordering of the input matrix. There are currently two algorithms for column reordering that are most effective for the search stage, referred to here as SW and CH. Although both use all available information in the problem, the SW and CH algorithms look different and were derived respectively from geometric and algebraic points of view. In this thesis we modify the SW algorithm to make it more computationally efficient and easier to comprehend. We then prove that the SW and CH algorithms actually give the same column reordering in theory. Finally, we propose a new mathematically equivalent algorithm, which is more computationally efficient and is still easy to understand. This thesis also extends the column permutation idea to ordinary integer least squares problems. A new reduction algorithm which combines the well-known Lenstra–Lenstra–Lovász (LLL) reduction and the new column reordering strategy is proposed. The new reduction can be much more effective than the LLL reduction in some cases. The thesis also reviews some common search algorithms. A new one is proposed, which is based on two previous algorithms, the depth-first search and the best-first search. This hybrid algorithm makes use of the advantages of both originals, is more efficient than either and is easier to implement than other previous hybrid algorithms.Cette thèse s'intéresse aux problèmes de moindres carrés entiers (ILS), ou les problèmes du vecteur le plus proche. Une approche souvent utilisée pour résoudre ces problèmes est la méthode de recherche discrète, qui implique deux étapes: la réduction et la recherche. Le but principal de la réduction est de rendre l'étape de recherche plus rapide. Les stratégies de réduction des problèmes ILS sous contrainte de boîte impliquent la réorganisation de colonnes de la matrice de données. Il existe actuellement deux algorithmes pour la réorganisation des colonnes, appelés ici les algorithmes SW et CH, qui sont les plus efficaces pour la phase de recherche. Bien que les deux utilisent toutes les informations disponibles dans le problème, les algorithmes SW et CH sont différents en apparence, et ont été obtenus respectivement à partir d'une point de vue géométrique et algébrique de vue. Dans cette thèse, nous modifions l'algorithme SW pour rendre son calcul plus efficace et plus facile à comprendre. Nous démontrons ensuite qu'en théorie, les algorithmes SW et CH donne effectivement la même réorganisation de colonnes. Enfin, nous proposons un nouveau algorithme mathématiquement équivalent qui est plus efficace, tout en demeurant facile à comprendre. Cette thèse étend également l'idée de permutation de colonnes aux problèmes ordinaires de moindres carrés entiers. Un nouveau algorithme de réduction qui combine le célèbre agorithme Lenstra-Lenstra-Lovász (LLL) avec la nouvelle stratégie de réorganisation de colonnes est proposé. La nouvelle réduction peut être plus efficace que la réduction LLL dans certains cas.Cette thèse examine également certains algorithmes de recherche d'usage courant. Un nouveau est proposé qui est basé sur deux algorithmes précédents: l'algorithme de parcours en profondeur et celui de la recherche au meilleur d'abord. Notre algorithme hybride détient les avantages des deux originaux, tout en étant plus efficace et plus facile à utiliser que d'autres algorithmes hybrides déjà existants.
28
Saadi, Kamel. "Efficient regularisation of least-squares kernel machines." Thesis, University of East Anglia, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.522281.
Full text
29
Rogers, C. A. "Partial least squares (PLS) : a comparative assessment." Thesis, University of Bath, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235583.
Full text
30
Cho, Youngjae. "Least squares estimation of acoustic reflection coeffficient." Thesis, University of Southampton, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420208.
Full text
31
TORTURELA, ALEXANDRE DE MACEDO. "NOVEL SPARSE SYSTEMS LEAST SQUARES ESTIMATION METHODS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26712@1.
Full textAbstract:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROINSTITUTO MILITAR DE ENGENHARIA
CENTRO TECNOLÓGICO DO EXÉRCITO
INSTITUTO DE PESQUISA E DESENVOLVIMENTO
Neste trabalho, quatro métodos projetados especificamente para a estimação de sistemas esparsos são originalmente elaborados e apresentados. São eles: Encolhimentos Sucessivos, Expansões Sucessivas, Minimização da Norma l1 e Ajuste Automático do fator de regularização do Custo LS. Os quatro métodos propostos baseiam-se na técnica de estimação de sistemas lineares e invariantes no tempo pelo critério dos mínimos quadrados, universalmente conhecida por sua denominação em inglês - Least Squares (LS) Estimation, e incorporam técnicas relacionadas a otimização convexa e à teoria de compressive sensing. Os resultados obtidos em simulações mostram que os métodos em questão têm desempenho superior que a estimação LS convencional e que o algoritmo Recursive Least Squares (RLS) com regularização convexa denominado l1-RLS, em muitos casos alcançando o desempenho ótimo apresentado pelo método de estimação LS Oráculo, no qual o suporte da resposta ao impulso em tempo discreto do sistema estimado é conhecido a priori. Além disso, os métodos propostos apresentam custo computacional menor que do algoritmo l1-RLS.
In this thesis, four methods specifically designed for sparse systems estimation are originally developed and presented, which were called here: Relaxations method, Successive Expansions method, l1-norm Minimization method and Automatic Adjustment of the Regularization Factor method. The four proposed methods are based on the Least Squares (LS) Estimation method and incorporate techniques related to convex optimization and to the theory of compressive sensing. The simulation results show that the proposed methods herein present superior performance than the ordinary LS estimation method and the Recursive Least Squares (RLS) with convex regularization method (l1-RLS), in many cases achieving the same optimal performance presented by the LS Oracle method. Furthermore, the proposed methods demand lower computational cost than the l1-RLS method.
32
Bian, Xiaomeng. "Completely Recursive Least Squares and Its Applications." ScholarWorks@UNO, 2012. http://scholarworks.uno.edu/td/1518.
Full textAbstract:
The matrix-inversion-lemma based recursive least squares (RLS) approach is of a recursive form and free of matrix inversion, and has excellent performance regarding computation and memory in solving the classic least-squares (LS) problem. It is important to generalize RLS for generalized LS (GLS) problem. It is also of value to develop an efficient initialization for any RLS algorithm.
In Chapter 2, we develop a unified RLS procedure to solve the unconstrained/linear-equality (LE) constrained GLS. We also show that the LE constraint is in essence a set of special error-free observations and further consider the GLS with implicit LE constraint in observations (ILE-constrained GLS).
Chapter 3 treats the RLS initialization-related issues, including rank check, a convenient method to compute the involved matrix inverse/pseudoinverse, and resolution of underdetermined systems. Based on auxiliary-observations, the RLS recursion can start from the first real observation and possible LE constraints are also imposed recursively. The rank of the system is checked implicitly. If the rank is deficient, a set of refined non-redundant observations is determined alternatively.
In Chapter 4, base on [Li07], we show that the linear minimum mean square error (LMMSE) estimator, as well as the optimal Kalman filter (KF) considering various correlations, can be calculated from solving an equivalent GLS using the unified RLS.
In Chapters 5 & 6, an approach of joint state-and-parameter estimation (JSPE) in power system monitored by synchrophasors is adopted, where the original nonlinear parameter problem is reformulated as two loosely-coupled linear subproblems: state tracking and parameter tracking. Chapter 5 deals with the state tracking which determines the voltages in JSPE, where dynamic behavior of voltages under possible abrupt changes is studied. Chapter 6 focuses on the subproblem of parameter tracking in JSPE, where a new prediction model for parameters with moving means is introduced. Adaptive filters are developed for the above two subproblems, respectively, and both filters are based on the optimal KF accounting for various correlations. Simulations indicate that the proposed approach yields accurate parameter estimates and improves the accuracy of the state estimation, compared with existing methods.
33
Schwab, Devin. "Hierarchical Sampling for Least-Squares Policy Iteration." Case Western Reserve University School of Graduate Studies / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=case1441374844.
Full text
34
Chatkupt, Chlump. "Least-squares regret and partially strategic players." Thesis, London School of Economics and Political Science (University of London), 2015. http://etheses.lse.ac.uk/3220/.
Full textAbstract:
Noncooperative game theory enjoys a vast canon of solution concepts. The predominant solution concept is Nash equilibrium (Nash, 1950a; Nash, 1951). Other solution concepts include generalizations and refinements of Nash equilibrium as well as alternatives to it. Despite their successes, the established solution concepts are in some ways unsatisfactory. In particular, for many games, such as the Centipede Game (Rosenthal, 1981), the p-Beauty Contest (Moulin, 1986; Simonsen, 1988), and the notorious Traveler’s Dilemma (Basu, 1994; Basu, 2007), many of the solution concepts yield solutions that are both unreasonable in theory and refuted by the experimental evidence. And when a solution concept manages to yield the expected or reasonable solutions for such games, it often suffers from other difficulties such as unwieldy complexity or reliance on ad hoc or game-specific constructions that may fail to be generalizable. We propose a new solution concept, which we call least-squares regret, that yields the expected or reasonable solutions for games that have thus far proved to be problematic, such as the Traveler’s Dilemma; that is simple; that involves no ad hoc or game-specific constructions and can thus be applied immediately and consistently to any arbitrary game; that exhibits nice properties; and that is grounded in human psychology. Intuitively, we suppose that a player chooses a strategy so as to minimize the divergence from perfect play overall. In particular, we suppose that a player is partially strategic and chooses a strategy so as to minimize the sum, across all partial profiles of strategies of the other players, of the squares of the regrets, where the regret of a strategy with respect to a partial profile is the difference of the best-response payoff with respect to the partial profile and the payoff from choosing the strategy with respect to the partial profile. The aim of this work is to develop the solution concept of least-squares regret; explore its properties; assess its performance with respect to various games of interest; determine its merits and demerits, especially in relation to other solution concepts; review its weaknesses; introduce a refinement, which we call mutual weighted least-squares regret, that addresses some of the weaknesses; and propose some questions for further research.
35
Rosopa, Patrick. "A COMPARISON OF ORDINARY LEAST SQUARES, WEIGHTED LEAST SQUARES, AND OTHER PROCEDURES WHEN TESTING FOR THE EQUALITY OF REGRESSION." Doctoral diss., University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2311.
Full textAbstract:
When testing for the equality of regression slopes based on ordinary least squares (OLS) estimation, extant research has shown that the standard F performs poorly when the critical assumption of homoscedasticity is violated, resulting in increased Type I error rates and reduced statistical power (Box, 1954; DeShon & Alexander, 1996; Wilcox, 1997). Overton (2001) recommended weighted least squares estimation, demonstrating that it outperformed OLS and performed comparably to various statistical approximations. However, Overton's method was limited to two groups. In this study, a generalization of Overton's method is described. Then, using a Monte Carlo simulation, its performance was compared to three alternative weight estimators and three other methods. The results suggest that the generalization provides power levels comparable to the other methods without sacrificing control of Type I error rates. Moreover, in contrast to the statistical approximations, the generalization (a) is computationally simple, (b) can be conducted in commonly available statistical software, and (c) permits post hoc analyses. Various unique findings are discussed. In addition, implications for theory and practice in psychology and future research directions are discussed.Ph.D.
Department of Psychology
Sciences
Psychology
36
Holmes, Marion R. "Least squares approximation by G¹ piecewise parametric cubics /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1993. http://handle.dtic.mil/100.2/ADA277978.
Full text
37
Huang, Xuejun, and Xuewen Huang. "The Least-Squares Method for American Option Pricing." Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119754.
Full text
38
Munoz, Maldonado Yolanda. "Mixed models, posterior means and penalized least squares." Texas A&M University, 2005. http://hdl.handle.net/1969.1/2637.
Full textAbstract:
In recent years there has been increased research activity in the area of Func-
tional Data Analysis. Methodology from finite dimensional multivariate analysis has
been extended to the functional data setting giving birth to Functional ANOVA,
Functional Principal Components Analysis, etc. In particular, some studies have pro-
posed inferential techniques for various functional models that have connections to
well known areas such as mixed-effects models or spline smoothing. The methodol-
ogy used in these cases is computationally intensive since it involves the estimation of
coefficients in linear models, adaptive selection of smoothing parameters, estimation
of variances components, etc.
This dissertation proposes a wide-ranging modeling framework that includes
many functional linear models as special cases. Three widely used tools are con-
sidered: mixed-effects models, penalized least squares, and Bayesian prediction. We
show that, in certain important cases, the same numerical answer is obtained for these
seemingly different techniques. In addition, under certain assumptions, an applica-
tion of a Kalman filter algorithm is shown to improve the order of computations, by
two orders of magnitude, for point and interval estimates (with n being the sample
size). A functional data analysis setting is used to exemplify our results.
39
Botting, Brad. "Structured Total Least Squares for Approximate Polynomial Operations." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1035.
Full textAbstract:
This thesis presents techniques for accurately computing a number of fundamental operations on approximate polynomials. The general goal is to determine nearby polynomials which have a non-trivial result for the operation. We proceed by first translating each of the polynomial operations to a particular structured matrix system, constructed to represent dependencies in the polynomial coefficients. Perturbing this matrix system to a nearby system of reduced rank yields the nearby polynomials that have a non-trivial result. The translation from polynomial operation to matrix system permits the use of emerging methods for solving sophisticated least squares problems. These methods introduce the required dependencies in the system in a structured way, ensuring a certain minimization is met. This minimization ensures the determined polynomials are close to the original input. We present translations for the following operations on approximate polynomials: - Division
- Greatest Common Divisor (GCD)
- Bivariate Factorization
- Decomposition
40
Rossi, Michel. "Iterative least squares algorithms for digital filter design." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/10099.
Full textAbstract:
In this thesis, we propose new algorithms to simplify and improve the design of IIR digital filters and M-band cosine modulated filter banks. These algorithms are based on the Iterative Least Squares (ILS) approach. We first review the various Iterative Reweighted Least Squares (IRLS) methods used to design Chebyshev and $L\sb{p}$ linear phase FIR filters. Then we focus on the ILS design of IIR filters and filter banks. For the design of Chebyshev IIR filters in the log magnitude sense, we propose a Remez-type IRLS algorithm. This novel approach accelerates significantly Kobayashi's and Lim's IRLS methods and simplifies the traditional rational Remez algorithm. For the design of M-band cosine modulated filter banks, we propose three new ILS algorithms. These algorithms are specific to the design of Pseudo Quadrature Mirror Filter (QMF) banks, Near Perfect Reconstruction (NPR) Pseudo QMF banks and Perfect Reconstruction (PR) QMF banks. They are fast convergent, simple to implement and flexible compared to traditional nonlinear optimization methods. Short MATLAB programs implementing the proposed algorithms are included.
41
Skoglund, Ingegerd. "Algorithms for a Partially Regularized Least Squares Problem." Licentiate thesis, Linköping : Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-8784.
Full text
42
Abu, Safia Ahmed. "Phylogenetic inference by generalized least squares : computational aspects." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=97881.
Full textAbstract:
The generalized least squares (GLS) method for phylogenetic inference assumes that errors in observed distances have an approximately Gaussian distribution. GLS has not been widely used nor properly evaluated because of computational difficulties. We examine issues relating to the implementation of GLS. Different estimates for the covariance matrix are examined. We found that the matrix is often ill-conditioned. Methods for solving the ill-conditioned unconstrained least squares problem are compared in terms of stability and efficiency. We conclude that the normal equations method, with a modified covariance matrix, performs best. Versions of the nonnegative constrained GLS method are discussed, implemented, and evaluated. Curiously, the GLS method was less accurate than the simpler weighted least squares method. We compare Maximum Likelihood (ML) with least squares methods for selecting trees and we notice that GLS correlates well with ML on trees close to the true tree.
43
Lannsjö, Fredrik. "Forecasting the Business Cycle using Partial Least Squares." Thesis, KTH, Matematisk statistik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-151378.
Full textAbstract:
Partial Least Squares is both a regression method and a tool for variable selection, that is especially appropriate for models based on numerous (possibly correlated) variables. While being a well established modeling tool in chemometrics, this thesis adapts PLS to financial data to predict the movements of the business cycle represented by the OECD Composite Leading Indicators. High-dimensional data is used, and a model with automated variable selection through a genetic algorithm is developed to forecast different economic regions with good results in out-of-sample tests.Partial Least Squares är både en regressionsmetod och ett verktyg för variabelselektion som är specielltlämpligt för modeller baserade på en stor mängd (möjligtvis korrelerade) variabler.Medan det är en väletablerad modelleringsmetod inom kemimetri, anpassar den häruppsatsen PLS till finansiell data för att förutspå rörelserna av konjunkturen,representerad av OECD's Composite Leading Indicator. Högdimensionella dataanvänds och en model med automatiserad variabelselektion via en genetiskalgoritm utvecklas för att göra en prognos av olika ekonomiska regioner medgoda resultat i out-of-sample-tester
44
Holmes, Marion R. "Least squares approximation by G1 piecewise parametric cubics." Thesis, Monterey, California. Naval Postgraduate School, 1993. http://hdl.handle.net/10945/39690.
Full textAbstract:
Approved for public release; distribution is unlimited.Parametric piecewise cubic polynomials are used throughout the computer graphics industry to represent geometric curved shapes. The exploration of the use of parametric curves and surfaces can be viewed as the birth of Computer Aided Geometric Design (CAG
45
Gomez, Steven A. "Parallel multigrid for large-scale least squares sensitivity." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82481.
Full textAbstract:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from department-submitted PDF version of thesis
Includes bibliographical references (p. 85-86).
This thesis presents two approaches for efficiently computing the "climate" (long- time average) sensitivities for dynamical systems. Computing these sensitivities is essential to performing engineering analysis and design. The first technique is a novel approach to solving the "climate" sensitivity problem for periodic systems. A small change to the traditional adjoint sensitivity equations results in a method which can accurately compute both instantaneous and long-time averaged sensitivities. The second approach deals with the recently developed Least Squares Sensitivity (LSS) method. A multigrid algorithm is developed that can, in parallel, solve the discrete LSS system. This generic algorithm can be applied to ordinary differential equations such as the Lorenz System. Additionally, this parallel method enables the estimation of climate sensitivities for a homogeneous isotropic turbulence model, the largest scale LSS computation performed to date.
by Steven A. Gomez.
S.M.
46
Moller, Jurgen Johann. "The implementation of noise addition partial least squares." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/3362.
Full textAbstract:
Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2009.When determining the chemical composition of a specimen, traditional laboratory techniques are often both expensive and time consuming. It is therefore preferable to employ more cost effective spectroscopic techniques such as near infrared (NIR). Traditionally, the calibration problem has been solved by means of multiple linear regression to specify the model between X and Y. Traditional regression techniques, however, quickly fail when using spectroscopic data, as the number of wavelengths can easily be several hundred, often exceeding the number of chemical samples. This scenario, together with the high level of collinearity between wavelengths, will necessarily lead to singularity problems when calculating the regression coefficients. Ways of dealing with the collinearity problem include principal component regression (PCR), ridge regression (RR) and PLS regression. Both PCR and RR require a significant amount of computation when the number of variables is large. PLS overcomes the collinearity problem in a similar way as PCR, by modelling both the chemical and spectral data as functions of common latent variables. The quality of the employed reference method greatly impacts the coefficients of the regression model and therefore, the quality of its predictions. With both X and Y subject to random error, the quality the predictions of Y will be reduced with an increase in the level of noise. Previously conducted research focussed mainly on the effects of noise in X. This paper focuses on a method proposed by Dardenne and Fernández Pierna, called Noise Addition Partial Least Squares (NAPLS) that attempts to deal with the problem of poor reference values. Some aspects of the theory behind PCR, PLS and model selection is discussed. This is then followed by a discussion of the NAPLS algorithm. Both PLS and NAPLS are implemented on various datasets that arise in practice, in order to determine cases where NAPLS will be beneficial over conventional PLS. For each dataset, specific attention is given to the analysis of outliers, influential values and the linearity between X and Y, using graphical techniques. Lastly, the performance of the NAPLS algorithm is evaluated for various
47
Kumar, Rajendra. "FAST FREQUENCY ACQUISITION VIA ADAPTIVE LEAST SQUARES ALGORITHM." International Foundation for Telemetering, 1986. http://hdl.handle.net/10150/615276.
Full textAbstract:
International Telemetering Conference Proceedings / October 13-16, 1986 / Riviera Hotel, Las Vegas, NevadaA new least squares algorithm is proposed and investigated for fast frequency and phase acquisition of sinusoids in the presence of noise. This algorithm is a special case of more general adaptive parameter estimation techniques. The advantages of the algorithms are their conceptual simplicity, flexibility and applicability to general situations. For example, the frequency to be acquired can be time varying, and the noise can be non-gaussian, nonstationary and colored. As the proposed algorithm can be made recursive in the number of observations, it is not necessary to have a-priori knowledge of the received signal-to-noise ratio or to specify the measurement time. This would be required for batch processing techniques, such as the Fast Fourier Transform (FFT). The proposed algorithm improves the frequency estimate on a recursive basis as more and more observations are obtained. When the algorithm is applied in real time, it has the extra advantage that the observations need not be stored. The algorithm also yields a real time confidence measure as to the accuracy of the estimator.
48
Woodard, Joseph Walker. "The Linear Least Squares Problem of Bundle Adjustment." UNF Digital Commons, 1990. http://digitalcommons.unf.edu/etd/227.
Full textAbstract:
A method is described for finding the least squares solution of the overdetermined linear system that arises in the photogrammetric problem of bundle adjustment of aerial photographs. Because of the sparse, blocked structure of the coefficient matrix of the linear system, the proposed method is based on sparse QR factorization using Givens rotations. A reordering of the rows and columns of the matrix greatly reduces the fill-in during the factorization. Rules which predict the fill-in for this ordering are proven based upon the block structure of the matrix. These rules eliminate the need for the usual symbolic factorization in most cases. A subroutine library that implements the proposed method is listed. Timings and populations of a range of test problems are given.
49
Oyedele, Opeoluwa Funmilayo. "The construction of a partial least squares biplot." Doctoral thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/12948.
Full textAbstract:
Includes bibliographical references.In multivariate analysis, data matrices are often very large, which sometimes makes it difficult to describe their structure and to make a visual inspection of the relationship between their respective rows (samples) and columns (variables). For this reason, biplots, the joint graphical display of the rows and columns of a data matrix, can be useful tools for analysis. Since they were first introduced, biplots have been employed in a number of multivariate methods, such as Correspondence Analysis (CA), Principal Component Analysis (PCA), Canonical Variate Analysis (CVA) and Discriminant Analysis (DA), as a form of graphical display of data. Another possible employment is in Partial Least Squares (PLS). First introduced as a regression method, PLS is more flexible than multivariate regression, but better suited than Principal Component Regression (PCR) for the prediction of a set of response variables from a large set of predictor variables. Employing the biplot in PLS gave rise to the PLS biplot, a new addition to the biplot family. In the current study, this biplot was successfully applied to the sensory data to investigate the relationships between the sensory panel characteristics and the chemical quality measurements of sixteen olive oils. It was also applied to a large set of mineral sorting production data to investigate the relationships between the output variables and the process factors used to produce a final product. Furthermore, the PLS biplot was applied to a Binomialdistributed data concerning the diabetes testing of Indian women and to a Poisson-distributed data showing the diversity of arboreal marsupials (possum) in the Montane ash forest. After these applications, it is proposed that the PLS biplot is a useful graphical tool for displaying results from the (univariate) Partial Least Squares-Generalized Linear Model (PLS-GLM) analysis of a data set. With Partial Least Squares Regression (PLSR) being a valuable method for modelling high-dimensional data, especially in chemometrics, the PLS biplot was successfully applied to a cereal evaluation containing one hundred and forty five infrared spectra and six chemical properties, and a gene expression data with two thousand genes.
50
Wang, Zhen. "Semi-parametric Bayesian Models Extending Weighted Least Squares." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1236786934.
Full text