L’étude des modèles de mélanges est un champ très vaste en statistique. Nous présentons dans la première partie de la thèse les phi-divergences et les méthodes existantes qui construisent des estimateurs robustes basés sur des phi-divergences. Nous nous intéressons en particulier à la forme duale des phi-divergences et nous construisons un nouvel estimateur robuste basant sur cette formule. Nous étudions les propriétés asymptotiques de cet estimateur et faisons une comparaison numérique avec les méthodes existantes. Dans un seconde temps, nous introduisons un algorithme proximal dont l’objectif est de calculer itérativement des estimateurs basés sur des critères de divergences statistiques. La convergence de l’algorithme est étudiée et illustrée par différents exemples théoriques et sur des données simulées. Dans la deuxième partie de la thèse, nous construisons une nouvelle structure pour les modèles de mélanges à deux composantes dont l’une est inconnue. La nouvelle approche permet d’incorporer une information a priori linéaire de type moments ou L-moments. Nous étudions les propriétés asymptotiques des estimateurs proposés. Des simulations numériques sont présentées afin de montrer l’avantage de la nouvelle approche en comparaison avec les méthodes existantes qui ne considèrent pas d’information a priori à part une hypothèse de symétrie sur la composante inconnue. / The study of mixture models constitutes a large domain of research in statistics. In the first part of this work, we present phi-divergences and the existing methods which produce robust estimators. We are more particularly interested in the so-called dual formula of phi-divergences. We build a new robust estimator based on this formula. We study its asymptotic properties and give a numerical comparison with existing methods on simulated data. We also introduce a proximal-point algorithm whose aim is to calculate divergence-based estimators. We give some of the convergence properties of this algorithm and illustrate them on theoretical and simulated examples. In the second part of this thesis, we build a new structure for two-component mixture models where one component is unknown. The new approach permits to incorporate a prior linear information about the unknown component such as moment-type and L-moments constraints. We study the asymptotic properties of the proposed estimators. Several experimental results on simulated data are illustrated showing the advantage of the novel approach and the gain from using the prior information in comparison to existing methods which do not incorporate any prior information except for a symmetry assumption over the unknown component.

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This thesis deals with trading using technical analysis. Mostly attention is paid shares traded on the Prague Stock Exchange. The practical part describes computer program, which gives recommendations for the purchase and sale of shares based on moving averages and methods of moving average convergence / divergence and relative strength index. The conclusion is stated financial comparison of the methods.

Master's thesis is focused on solution of the statistical problem to find a probability distribution of a discrete random variable on the basis of the observed data. These estimates are obtained by minimizing pseudo-quasinorm which is introduced here.The thesis further focuses on atributes of this pseudo-quasinorm. It also contains practical application of these methods.

abstract: Deep neural networks (DNNs) have had tremendous success in a variety of statistical learning applications due to their vast expressive power. Most applications run DNNs on the cloud on parallelized architectures. There is a need for for efficient DNN inference on edge with low precision hardware and analog accelerators. To make trained models more robust for this setting, quantization and analog compute noise are modeled as weight space perturbations to DNNs and an information theoretic regularization scheme is used to penalize the KL-divergence between perturbed and unperturbed models. This regularizer has similarities to both natural gradient descent and knowledge distillation, but has the advantage of explicitly promoting the network to and a broader minimum that is robust to weight space perturbations. In addition to the proposed regularization, KL-divergence is directly minimized using knowledge distillation. Initial validation on FashionMNIST and CIFAR10 shows that the information theoretic regularizer and knowledge distillation outperform existing quantization schemes based on the straight through estimator or L2 constrained quantization. / Dissertation/Thesis / Masters Thesis Computer Engineering 2019

The area of ASEAN countries and the subsequent role of regionalisation were being analysed in this thesis whilst employing the HDI, mortality rate up to 5 years, life expectancy at birth, GDP per capita, unemployment rate, and FDI as the crucial indicators. The study aims to examine the ASEAN countries and its aggregation within both the economic and social spheres. A 10-year period (2006-2016) had been inquired so that the development of each indicator may be examined. And therefore, results of beta convergence could be displayed in a correlation diagrams. The convergence trend has mirrored in five indicators. The only indicator, however, to be diverging has been represented by the unemployment rate. The findings of beta convergence suggest that, in comparison with economic indicators, social indicators tend to converge in a more significant manner in the ASEAN countries.

This diploma thesis examines the influence of the economic crisis from 2008-2009 on the convergence of the regions of the Czech Republic defined at NUTS 3 level. Trends in region convergence are identified based on the beta convergence and sigma convergence analysis using panel data from 2002-2015. Subsequently are discussed the reasons for the observed differences and the consequences of unequal economic development in the regions for private companies that are located or are operating in the regions.

<p>Predmet istraživanja ovog rada je istraživanje i eksploatacija mogućnosti da parametri Gausovih komponenti korišćenih Gaussian mixture modela&nbsp; (GMM) aproksimativno leže na niže dimenzionalnoj površi umetnutoj u konusu pozitivno definitnih matrica. U tu svrhu uvodimo novu, mnogo efikasniju meru sličnosti između GMM-ova projektovanjem LPP-tipa parametara komponenti iz više dimenzionalnog parametarskog originalno konfiguracijskog prostora u prostor značajno niže dimenzionalnosti. Prema tome, nalaženje distance između dva GMM-a iz originalnog prostora se redukuje na nalaženje distance između dva skupa niže dimenzionalnih euklidskih vektora, ponderisanih odgovarajućim težinama. Predložena mera je pogodna za primene koje zahtevaju visoko dimenzionalni prostor obeležja i/ili veliki ukupan broj Gausovih komponenti. Razrađena metodologija je primenjena kako na sintetičkim tako i na realnim eksperimentalnim podacima.</p> / <p>This thesis studies the possibility that the parameters of Gaussian components of a<br />particular Gaussian Mixture Model (GMM) lie approximately on a lower-dimensional<br />surface embedded in the cone of positive definite matrices. For that case, we deliver<br />novel, more efficient similarity measure between GMMs, by LPP-like projecting the<br />components of a particular GMM, from the high dimensional original parameter space,<br />to a much lower dimensional space. Thus, finding the distance between two GMMs in<br />the original space is reduced to finding the distance between sets of lower<br />dimensional euclidian vectors, pondered by corresponding weights. The proposed<br />measure is suitable for applications that utilize high dimensional feature spaces and/or<br />large overall number of Gaussian components. We confirm our results on artificial, as<br />well as real experimental data.</p>

So far, research on inter- and intraspecific teleost brain plasticity across different freshwater environments has been widely conducted. However, insights of brain morphological variation on social and predator avoidance behaviours are lacking. Here, we investigated variation in shape and size of the brain and its six major regions of European minnows (Phoxinus phoxinus) inhabiting Lake Ånnsjön and its tributaries, using geometric morphometrics methods. We also experimentally compared stream and lake fish activity and social behaviour under different feeding and predation regimes. Contrary to our predictions of lake minnows having evolved smaller brains because of living in habitats with reduced environmental complexity compared to their conspecifics in the streams, we found that overall brain size generally did not differ between locations. Instead, brain morphology differed between minnows caught in the lake and streams, with stream minnows showing larger dorsal medulla, telencephalon and olfactory bulbs, and lake minnows presenting larger optic tecta and hypothalamus. Experimental results showed that lake minnows were more likely to engage in social behaviour than those from streams. Our results indicate that while overall allocation of energy to the brain does not change, habitat-specific differences in activity and trophic divergence might predict specialization for different senses, allocating more resources towards different brain regions. In addition, we show how various ecological factors, such as environmental complexity and social organization seem to be reflected in brain shape.

Dissertation thesis is focused on solution of the statistical problem to find a probability distribution of a discrete random variable on the basis of the observed data. These estimates are obtained by minimizing quasi-norms with given constraints. The thesis further focuses on deriving confidence intervals for estimated probabilities. It also contains practical application of these methods.