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Regularization techniques based on the least squares method
Kubínová, Marie ; Hnětynková, Iveta (advisor)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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Regression for High-Dimensional Data: From Regularization to Deep Learning
Kalina, Jan ; Vidnerová, Petra
Regression modeling is well known as a fundamental task in current econometrics. However, classical estimation tools for the linear regression model are not applicable to highdimensional data. Although there is not an agreement about a formal definition of high dimensional data, usually these are understood either as data with the number of variables p exceeding (possibly largely) the number of observations n, or as data with a large p in the order of (at least) thousands. In both situations, which appear in various field including econometrics, the analysis of the data is difficult due to the so-called curse of dimensionality (cf. Kalina (2013) for discussion). Compared to linear regression, nonlinear regression modeling with an unknown shape of the relationship of the response on the regressors requires even more intricate methods.
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Regularization properties of Krylov subspace methods
Kučerová, Andrea ; Hnětynková, Iveta (advisor) ; Kučera, Václav (referee)
The aim of this thesis is to study and describe regularizing properties of iterative Krylov subspace methods for finding a solution of linear algebraic ill- posed problems contaminated by white noise. First we explain properties of this kind of problems, especially their sensitivity to small perturbations in data. It is shown that classical methods for solving approximation problems (such as the least squares method) fail here. Thus we turn to explanation of regularizing pro- perties of projections onto Krylov subspaces. Basic Krylov regularizing methods are considered, namely RRGMRES, CGLS, and LSQR. The results are illustrated on model problems from Regularization toolbox in MATLAB. 1
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Regularization methods for discrete inverse problems in single particle analysis
Havelková, Eva ; Hnětynková, Iveta (advisor) ; Plešinger, Martin (referee)
The aim of this thesis is to investigate applicability of regulariza- tion by Krylov subspace methods to discrete inverse problems arising in single particle analysis (SPA). We start with a smooth model formulation and describe its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a lin- ear operator and b represents the measured noisy data. We provide theoretical background and overview of selected methods for the solution of general linear inverse problems. Then we focus on specific properties of inverse problems from SPA, and provide experimental analysis based on synthetically generated SPA datasets (experiments are performed in the Matlab enviroment). Turning to the solution of our inverse problem, we investigate in particular an approach based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable stopping criterion for the iterative part as well as parameter-choice method for the inner regularization are discussed. Providing a complete implementation of the proposed solver (in Matlab and in C++), its performance is evaluated on various SPA model datasets, considering high levels of noise and realistic distri- bution of orientations of scanning angles. Comparison to other regularization methods, including the ART method traditionally used in SPA,...
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Using Adversarial Examples in Natural Language Processing
Bělohlávek, Petr ; Žabokrtský, Zdeněk (advisor) ; Libovický, Jindřich (referee)
Machine learning has been paid a lot of attention in recent years. One of the studied fields is employment of adversarial examples. These are artifi- cially constructed examples which evince two main features. They resemble the real training data and they deceive already trained model. The ad- versarial examples have been comprehensively investigated in the context of deep convolutional neural networks which process images. Nevertheless, their properties have been rarely examined in connection with NLP-processing networks. This thesis evaluates the effect of using the adversarial examples during the training of the recurrent neural networks. More specifically, the main focus is put on the recurrent networks whose text input is in the form of a sequence of word/character embeddings, which have not been pretrained in advance. The effects of the adversarial training are studied by evaluating multiple NLP datasets with various characteristics.
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Regularization techniques based on the least squares method
Kubínová, Marie ; Hnětynková, Iveta (advisor)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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Regularizační metody založené na metodách nejmenších čtverců
Michenková, Marie ; Hnětynková, Iveta (advisor) ; Zítko, Jan (referee)
Title: Regularization Techniques Based on the Least Squares Method Author: Marie Michenková Department: Department of Numerical Mathematics Supervisor: RNDr. Iveta Hnětynková, Ph.D. Abstract: In this thesis we consider a linear inverse problem Ax ≈ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown in [Hnětynková, Plešinger, Strakoš, 2009] that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We propose a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b. This method is tested for different types of noise. Further, Hnětynková, Plešinger, and Strakoš provided an estimator of the noise level in the data. We propose a modification of this estimator based on the knowledge of the point of noise revealing. Keywords: ill-posed problems, regularization, Golub-Kahan iterative bidiagonalization, noise revealing, noise estimate, denoising 1
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Blind Image Deconvolution of Electron Microscopy Images
Schlorová, Hana ; Odstrčilík, Jan (referee) ; Walek, Petr (advisor)
V posledních letech se metody slepé dekonvoluce rozšířily do celé řady technických a vědních oborů zejména, když nejsou již limitovány výpočetně. Techniky zpracování signálu založené na slepé dekonvoluci slibují možnosti zlepšení kvality výsledků dosažených zobrazením pomocí elektronového mikroskopu. Hlavním úkolem této práce je formulování problému slepé dekonvoluce obrazů z elektronového mikroskopu a hledání vhodného řešení s jeho následnou implementací a porovnáním s dostupnou funkcí Matlab Image Processing Toolboxu. Úplným cílem je tedy vytvoření algoritmu korigujícícho vady vzniklé v procesu zobrazení v programovém prostředí Matlabu. Navržený přístup je založen na regularizačních technikách slepé dekonvoluce.
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Regularization of Illegal Migration as a Policy-making Process
Dumont, Anna ; Novotný, Vilém (advisor) ; Jelínková, Marie (referee)
'Regularization of Illegal Migration as a Policy-making Process' deals with the social problem of having a high number of irregular migrants in the Czech Republic and regularization as a tool that could help reduce it. Regularization is seen as a political process theoretically described by using the Advocacy Coalition Framework. This thesis tries to find normative definitions of the two coalitions, which hold different beliefs and two different points of view rather than describe the problem. The work is partly designed as a case study in which the theory is applied to the issue of regularization in part there is also an explanation of regularization as well as the Advocacy Coalition Framework. The thesis defines the two coalitions within the subsystem - the for-regularization and anti-regularization coalitions. Each coalition has its deep core and policy core beliefs that determine the relationship to the topic as well as the relationship between the coalitions themselves. In conclusion, the author summarized the information about the coalitions and their belief in three comparative tables where one can confront their approaches. The last part also contains a chapter on The Changes of Beliefs and Policies, where there is an introduction of two policies: the system of voluntary return and that...
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