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# Topic: Regularization

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 Tikhonov regularization - Wikipedia, the free encyclopedia Tikhonov regularization is the most commonly used method of regularization of ill-posed problems. Although at first the choice of the solution to this regularized problem may look artificial, and indeed the parameter α seems rather arbitrary, the process can be justified in a Bayesian point of view. This demonstrates the effect of the Tikhonov parameter on the condition number of the regularized problem. en.wikipedia.org /wiki/Tikhonov_regularization   (866 words)

 Regularization - Wikipedia, the free encyclopedia The mathematical term regularization has two main meanings, both associated with making a mathematical more 'regular' or smooth. In linguistics, regularization is the process of making irregular forms regular (e.g., "oxen" becomes "oxes;" "grew" becomes "growed"). Regularization is also the act of giving legal residency and identity documents to an illegal alien. en.wikipedia.org /wiki/Regularization   (125 words)

 Fa-Hsuan Lin : Research : Inverse : Projects - Regularization The regularization parameter characterizes the relative weights of data and current prior error terms in the cost function to be minimized. One choice of regularization parameter is the inverse of the SNR in the data. The regularization parameter was proposed to be the inverse of the SNR of the inverse as www.nmr.mgh.harvard.edu /~fhlin/research_inverse_project_regularization.htm   (1337 words)

 Migration Information Source - Why Countries Continue to Consider Regularization Regularization programs have risen in concert with the growth of unauthorized immigration; however, there is no consensus among states on the way to regularize migrants, and which migrants should be eligible. Thus, although regularization was a very unpopular idea in Greece, public opposition was outweighed by the country's need to control the estimated 16 to 20 percent of its population working in the informal economy. In Spain, the ILO reported that its first regularization process in 1985 resulted in widespread discrimination and exploitation of the immigrant labor force as some employers fired workers who asked to be formally hired or continued to employ them irregularly once the regularization process was underway. www.migrationinformation.org /Feature/display.cfm?id=330   (3341 words)

 Regularization: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-18) In mathematics, a function is a relation, such that each element (mathematics)element of a set (the domain) is associated with a unique element of... Regularization is the first step towards obtaining a completely finite and meaningful result; in quantum field theory quantum field theory quick summary: In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.... www.absoluteastronomy.com /encyclopedia/r/re/regularization.htm   (992 words)

 Regularization   (Site not responding. Last check: 2007-10-18) One of important issues in regularization is choosing optimal weight(or regularization parameter). Existing methods for choosing regularization parameters either require the prior information on noise in the data, or are heuristic graphical methods. In this work we apply a new method for choosing near-optimal regularization parameters by approximately minimizing the distance between the true solution and the family of regularized solutions. www.cs.umd.edu /~yangcj/node5.html   (106 words)

 SSP&A, Inc. PEST Freeware - Regularization   (Site not responding. Last check: 2007-10-18) The introduction of regularization capabilities to PEST brings with it tremendous benefits when calibrating most types of environmental models. In this way, you don't have to guess where such heterogeneity is required through the use of a cumbersome zonation pattern based on the artificial concept of "piecewise constancy". When using PEST in regularization mode you can estimate a large number of parameters, in each case supplying an item of "prior information" in the form of a preferred value for that parameter. www.sspa.com /pest/regul.html   (454 words)

 8.2 Regularization ambiguities   (Site not responding. Last check: 2007-10-18) By standard Hadamard regularization we mean the regularization based solely on the definitions of the partie finie of a singular function, Eq. This new regularization is mathematically well-defined and free of ambiguities; in particular it yields unique results for the computation of any of the integrals occuring in the 3PN equations of motion. [62] argue, clearing up the ambiguity is made possible by the fact that the dimensional regularization, contrary to the Hadamard regularization, respects all the basic properties of the algebraic and differential calculus of ordinary functions. www.maths.tcd.ie /EMIS/journals/LRG/Articles/Volume5/2002-3blanchet/node21.html   (922 words)

 Regularization Learning and Early Stopping in Linear Networks   (Site not responding. Last check: 2007-10-18) Generally, learning is performed to minimize the sum of squared errors between network outputs and training data. Then, the estimates of the optimal regularization parameter and the optimal stopping time are present and simple numerical simulations examine those. Moreover, for the choice of regularization parameter, the relationship between the Bayesian framework and the generalization error minimization framework is discussed. csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/ijcnn/2000/0619/04/0619toc.xml&DOI=10.1109/IJCNN.2000.860822   (275 words)

 Typographic Regularization in the WWP Textbase The Women Writers Project uses SGML tagging to encode a regularized spelling for such typographical variants, thereby allowing the option to display and search on either the original form or the regularized form. The wordlist-based program matches whole words with a dictionary list of known forms requiring regularization and replaces the word in the text with a form containing appropriate markup. The pattern-matching component uses a set of regular expressions to identify probable candidates for regularization that have not been found on the wordlist. www.nyu.edu /its/humanities/ach_allc2001/papers/russom   (877 words)

 KARACHI: Regularization of buildings -DAWN - Local; 15 September, 2004 The distinguished aspect of this scheme is its low fees contrary to that of the regularization scheme introduced by the provincial government. Those who had purchased flats in buildings, constructed in violation of building plans, would now be able to regularize their flats just after paying the fees for their flat. Earlier, the regularization of entire building was a pre-requisite, which was difficult usually due to disappearance of the builder after construction. www.dawn.com /2004/09/15/local3.htm   (256 words)

 Three-dimensional seismic data regularization I formulate data regularization as a linear-estimation problem and solve it with an iterative optimization algorithm. Smoothly varying surfaces are regularized with recursive helical smoothers based on the tension-spline theory. Alternatively, seismic data can be regularized with offset-continuation filters, which operate efficiently in frequency slices and bring information from neighboring offsets. sepwww.stanford.edu /public/docs/sep107/paper_html   (423 words)

 Regularization in Statistics   (Site not responding. Last check: 2007-10-18) In theoretical statistics, regularization is usually interpreted either in Bayesian terms, or as some form of Stein-like shrinkage. In applied statistics, regularization - often identified as ``penalty-based methods'', ``soft thresholding'' - is associated primarily with nonparametric regression and density estimation, often referred to rather imprecisely as ``smoothing''. In applications, regularization offers a unifying perspective on many diverse ill-posed inverse problems, a wide range of problems concerned with recovering information from indirect and usually noisy measurements, arising in geophysics, stereology, tomography, climatology and econometrics. www.pims.math.ca /birs/workshops/2003/03w5089   (299 words)

 Regularization   (Site not responding. Last check: 2007-10-18) Relationships between regularization and smoothing splines for vision processing are investigated by [Terzopoulos 1986b ; Lee and Pavlidis 1987]. The second term, called the smoothness term or the regularizer,     imposes the a priori smoothness constraint on the solution. When the regularizer takes the form of the rod (1.61), it encodes the smoothness of planar surfaces (in 1D). www.cs.cornell.edu /~rdz/664/MRF_Book/Chapter_1/node28.html   (541 words)

 Regularization in Hilbert scales   (Site not responding. Last check: 2007-10-18) For solving linear ill-posed problems regularization methods are required when the available data include some noise. In the present paper regularized approximations are obtained by a general regularization scheme in Hilbert scales which include well-known regularization methods such as the method of Tikhonov regularization and its higher-order forms, spectral methods, asymptotical regularization and iterative regularization methods. For both the cases of high- and low-order regularization, we study a priori and a posteriori rules for choosing the regularization parameter and provide order optimal error bounds that characterize the accuracy of the regularized approximations. www.iop.org /Select/abstract/-group=issn/0266-5611/21/6/003   (232 words)

 mri Since the systems arising from image reconstruction methods are usually large and sparse, our research is mainly focused on iterative regularization methods, and in particular conjugate gradients type regularization methods, that are suitable for such systems. The study of regularization methods is mainly centred on the choice of the regularization parameter. Regularization of Large Discrete ill posed problems in image processing, Recent trends in Numerical analysis (ed. www.dm.unibo.it /~piccolom/ricerca/regul.html   (317 words)

 Regularization Despite their potential, regularization techniques are poorly understood and little used. Specifically, regularization aids decision-making logic based on the gradient (that is, the rate of change of a quantity over time) of indicators. While regularization is not a total solution to the problem, it can help resolve this dilemma. www.traders.com /Documentation/FEEDbk_docs/Archive/072003/Abstracts_new/Satchwell/satchwell.html   (423 words)

 Regularization Tools   (Site not responding. Last check: 2007-10-18) The software package Regularization Tools, Version 3.1 (for Matlab Version 6.0), consists of 53 documented Matlab functions for analysis and solution of discrete ill-posed problems (plus 5 additional files). By means of this package, the user can experiment with different regularization strategies, compare them, and draw conclusions that would otherwise require a major programming effort. The function pptsvd.m computes piecewise polynomial regularized solutions by means of the PP-TSVD algorithm. www2.imm.dtu.dk /~pch/Regutools/regutools.html   (294 words)

 CATHOLIC ENCYCLOPEDIA: Nestorius and Nestorianism At this assembly, the Antiochene Christology was affirmed and a canon of Beit Lapat permitting the marriage of the clergy was repeated. Though no permission is given to priests or bishops to marry (for this was contrary to the canons of the Eastern Church), yet the practice appears to have been winked at, possibly for the regularization of illicit unions. Barsaûma himself is said to have married a nun named Mamoé; but according to Mare, this was at the inspiration of King Peroz, and was only a nominal marriage, intended to ensure the preservation of the lady's fortune from confiscation. www.newadvent.org /cathen/10755a.htm   (5351 words)

 Optimization and Regularization Specifically, the intention is to generalize regularization methods for linear inverse problems to also handle nonlinear inverse problems. To solve this optimization problem two regularization methods are proposed: A Gauss-Newton Tikhonov regularized method and a minimum norm Gauss-Newton method. It is shown that both regularization methods converge to a minimum norm solution of the nonlinear problem. www.cs.umu.se /~jerry/reports/phd.html   (544 words)

 Regularization by Model Reparameterization 1] for their ``continuation approach.'' I'd like to suggest an adjustment of the objective function to allow faster convergence of regularization and the continuation approach. The global minimum of this norm is often flat, with little sensitivity to large variations in the model. A continuation approach to regularization for traveltime tomography. billharlan.com /pub/papers/regularization/regularization.html   (886 words)

 ZETA REGULARIZATION TECHNIQUES WITH APPLICATIONS This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. www.worldscibooks.com /physics/2065.html   (148 words)

 Amazon.com: Geophysical Inverse Theory and Regularization Problems (Methods in Geochemistry and Geophysics): Books: ...   (Site not responding. Last check: 2007-10-18) The book brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. The key connecting idea of these applied parts of the book is the analogy between the solutions of the forward and inverse problems in different geophysical methods. www.amazon.com /exec/obidos/tg/detail/-/0444510893?v=glance   (763 words)

 KARACHI: Regularization date extended -DAWN - Local; May 3, 2005 KARACHI, May 2: The city government on Monday further extended the date for one time regularization of buildings scheme up to June 30. According to a notification the extension was granted by City Nazim Niamatullah Khan in exercise of powers under the Sindh Building Control Ordinance, 1979 as authority and chief executive of the KBCA. The extension was allowed keeping in view the inconvenience of the public due to extraordinary rush for submission of applications for one time regularization of buildings scheme, the notification said.—APP www.dawn.com /2005/05/03/local18.htm   (113 words)

 Keith Price Bibliography Low Level Techniques, Sensors, Image Representation, Color -- Regularization, etc. Regularization has been compared to a neural network with one hidden layer. There are a lot of references, and this may really go with his relaxation papers. A presentation of the basics of regularization and what it is intended to solve. iris.usc.edu /Vision-Notes/bibliography/compute42.html   (1058 words)

 Tomaso Poggio - CV   (Site not responding. Last check: 2007-10-18) "Regularization Algorithms for Learning that are Equivalent to Multilayer Networks," (T. Poggio and F. Girosi). "Regularized Least Squares Classification," (Rifkin, R., G. Yeo and T. Poggio) In: Advances in Learning Theory: Methods, Model and Applications, NATO Science Series III: Computer and Systems Sciences, VIOS Press, Amsterdam, (Eds.) Suykens, Horvath, Basu, Micchelli and Vandewalle, Vol. "Regularization, Radial Basis Functions, and Recent Extensions of Networks for Learning," (F. Girosi and T. Poggio). cbcl.mit.edu /people/poggio/poggio-cv-web.htm   (14041 words)

 Elissa L. Newport We are also conducting studies of human learners acquiring musical and other nonlinguistic patterns, and of nonhuman primates attempting to learn the same materials, to see where sequential learning, and the constraints on such learning, differ across species and domains. Wonnacott, E., and Newport, E.L. Novelty and regularization: The effect of novel instances on rule formation. Hudson Kam, C.L., and Newport, E.L. Regularizing unpredictable variation: The roles of adult and child learners in language formation and change. www.bcs.rochester.edu /people/newport/newport.html   (1221 words)

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