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Approximation of functions continuous on compact sets by layered neural networks
Fojtík, Vít ; Hakl, František (advisor) ; Mrázová, Iveta (referee)
Despite abundant research into neural network applications, many areas of the under- lying mathematics remain largely unexplored. The study of neural network expressivity is vital for understanding their capabilities and limitations. However, even for shallow networks this topic is far from solved. We provide an upper bound on the number of neurons of a shallow neural network required to approximate a function continuous on a compact set with given accuracy. Dividing the compact set into small polytopes, we ap- proximate the indicator function of each of them by a neural network and combine these into an approximation of the target function. This method, inspired by a specific proof of the Stone-Weierstrass Theorem, is more general than previous bounds of this character, with regards to approximation of continuous functions. Also, it is purely constructive. 1
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Implementing incomplete inverse decomposition on graphical processing units
Dědeček, Jan ; Tůma, Miroslav (advisor) ; Hakl, František (referee)
The goal of this Thesis was to evaluate a possibility to solve systems of linear algebraic equations with the help of graphical processing units (GPUs). While such solvers for generally dense systems seem to be more or less a part of standard production libraries, the Thesis concentrates on this low-level parallelization of equations with a sparse system that still presents a challenge. In particular, the Thesis considers a specific algorithm of an approximate inverse decomposition of symmetric and positive definite systems combined with the conjugate gradient method. An important part of this work is an innovative parallel implementation. The presented experimental results for systems of various sizes and sparsity structures point out that the approach is rather promising and should be further developed. Summarizing our results, efficient preconditioning of sparse systems by approximate inverses on GPUs seems to be worth of consideration. Powered by TCPDF (www.tcpdf.org)
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The real estate appraisal as a collateral
Hakl, František Marian ; Dušek, David (advisor) ; Šrytr, Pavel (referee)
The real estate appraisal within the banking industry is a specific discipline. Hence, there is a lack of theoretical background, especially in the Czech language. The aim of this work has two main parts. Firstly, there are analysed potential valuation bases and concrete approaches which are offered. Secondly, it is focused on practical determination the market value and the collateral value of the real property, regarding the current approaches using in the Czech banking industry.
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Impact of increase in VAT rates on households in the Czech Republic from 2007 to 2012
Hakl, František Marian ; Slintáková, Barbora (advisor) ; Mikušová, Pavla (referee)
Increase in the Value added tax rates in the Czech Republic from 2007 to 2012 evokes discussion about the tax impact on the tax burden of households. Nowadays, it is possible to quantify the real tax impact on households thanks to data from The Expenditures and Consumption of households included in Household Budget Survey. The aim of the bachelor thesis is to analyse the tax burden of households in the Czech Republic in the period of time from 2007 to 2012. The thesis is focused on the progress of the tax burden of households by status of head of household and the comparison between the households and tax burden of chosen consumption. The results confirm the increase in the tax burden of households in the Czech Republic from 2007 to 2012 and the dependency of the tax burden of these households on the method of quantification.
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Nástroj pro vzdálené použití NNSU algoritmu pro separaci dat (uživatelský manuál)
Hakl, František
Tento manuál popisuje základní použití serveru NNSU (paralelní implementace neuronové sítě s přepínacími jednotkami), který umožnuje vzdálený přístup k implementaci algoritmu NNSU a jeho pilotní použití na separování dat zaslaných na server. Účelem této volně přístupné aplikace je otestování vhodnosti separátoru na separaci uživatelských dat. Obsahem tohoto uživatelského návodu jsou informace postačující k využívání NNSU serveru, které popisují zpusob práce s daty určenými k separaci, způsob definování použité neuronové sítě, zadání výpočtu a metody hodnocení výsledné kvality separace.
Fulltext: content.csg -  PDF
Plný tet: v1200-13 - PDF
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Statistical Expectation of High Energy Physics Data Sets Separation Algorithms
Hakl, František
Article focuses on the application of the basic results of the statistical learning theory known as Probabilistic Approximately Correct learning in the evaluation and post-processing of unique physical data obtained from the detectors of particle accelerators. The aim of this article is not direct separation of the measured data but evaluation of the appropriateness of separation methods used. The main principles and results of the PAC learning theory are briefly summarized, the main characteristics of selected multivariable data separation algorithms are studied from the VC-dimension point of view. Finally, based on actual data sets obtained from Tevatron D$\emptyset$ experiment, some practical hints for separation method selection and numerical computation are derived.
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Volatility of selected separators/classifiers wrt. data sets from field of particle physics
Jiřina, Marcel ; Hakl, František
We study the volatility, i.e. influence of random changes in data sets to overall separation/classification behavior of separators/classifiers. This is motivated by the fact, that simulated data and true data from ATLAS experiment may differ, and a question arises what if separators or cuts are optimized for simulated data, and then used for true data from the experiment. This behavior was studied using simulated data modified by artificial distortions of known size. We found that even slight change in data sets causes a little worse result than supposed but, surprisingly, even relatively large distortions give then nearly the same results. Only truly great variations cause degradation of separation quality of separator/classifier as well as of the cuts method.
Fulltext: content.csg - PDF
Plný tet: v1126-11 - PDF
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