In this thesis Generalized Additive Neural Networks (GANNs) are studied in the context of predictive Data Mining. A GANN is a novel neural network implementation of a Generalized Additive Model. Originally GANNs were constructed interactively by considering partial residual plots. This methodology involves subjective human judgment, is time consuming, and can result in suboptimal results. The newly developed automated construction algorithm solves these difficulties by performing model selection based on an objective model selection criterion. Partial residual plots are only utilized after the best model is found to gain insight into the relationships between inputs and the target. Models are organized in a search tree with a greedy search procedure that identifies good models in a relatively short time. The automated construction algorithm, implemented in the powerful SAS® language, is nontrivial, effective, and comparable to other model selection methodologies found in the literature. This implementation, which is called AutoGANN, has a simple, intuitive, and user-friendly interface. The AutoGANN system is further extended with an approximation to Bayesian Model Averaging. This technique accounts for uncertainty about the variables that must be included in the model and uncertainty about the model structure. Model averaging utilizes in-sample model selection criteria and creates a combined model with better predictive ability than using any single model. In the field of Credit Scoring, the standard theory of scorecard building is not tampered with, but a pre-processing step is introduced to arrive at a more accurate scorecard that discriminates better between good and bad applicants. The pre-processing step exploits GANN models to achieve significant reductions in marginal and cumulative bad rates. The time it takes to develop a scorecard may be reduced by utilizing the automated construction algorithm. / Thesis (Ph.D. (Computer Science))--North-West University, Potchefstroom Campus, 2006.

Submitted by Alisson de Carvalho Reinol null (alissoncarv@gmail.com) on 2017-07-18T15:03:51Z No. of bitstreams: 1 tese_alisson_final.pdf: 6086108 bytes, checksum: 610534618b19a1d27cfff678d44f1a4a (MD5) / Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-07-19T14:22:46Z (GMT) No. of bitstreams: 1 reinol_ac_dr_sjrp.pdf: 6086108 bytes, checksum: 610534618b19a1d27cfff678d44f1a4a (MD5) / Made available in DSpace on 2017-07-19T14:22:46Z (GMT). No. of bitstreams: 1 reinol_ac_dr_sjrp.pdf: 6086108 bytes, checksum: 610534618b19a1d27cfff678d44f1a4a (MD5) Previous issue date: 2017-07-05 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho, consideramos aspectos algébricos e dinâmicos de alguns problemas envolvendo superfícies algébricas invariantes em sistemas diferenciais polinomiais definidos em R³. Determinamos o número máximo de planos invariantes que um sistema diferencial quadrático pode ter e estudamos a realização e integrabilidade de tais sistemas. Fornecemos a forma normal para sistemas diferenciais com quádricas invariantes e estudamos de forma mais detalhada a dinâmica e integrabilidade de sistemas diferenciais quadráticos com um paraboloide elíptico como superfície algébrica invariante. Por fim, estudamos as consequências dinâmicas ao se perturbar um sistema diferencial, cujo espaço de fase é folheado por superfícies algébricas invariantes. Para tal, consideramos o sistema diferencial quadrático conhecido como sistema Sprott A, que depende de um parâmetro real a e apresenta comportamento caótico mesmo sem ter pontos de equilíbrio, tendo, assim, um hidden attractor para valores adequados do parâmetro a. Provamos que, para a=0, o espaço de fase desse sistema é folheado por esferas concêntricas invariantes. Utilizando a Teoria do Averaging e o Teorema KAM (Kolmogorov-Arnold-Moser), provamos que, para a>0 suficientemente pequeno, uma órbita periódica orbitalmente estável emerge de um equilíbrio do tipo zero-Hopf não isolado localizado na origem e que formam-se toros invariantes em torno desta órbita periódica. Concluímos que a ocorrência de tais fatos tem um papel importante na formação do hidden attractor. / In this work, we consider algebraic and dynamical aspects of some problems involving invariant algebraic surfaces in polynomial differential systems defined in R³. We determine the maximum number of invariant planes that a quadratic differential system can have and we study the realization and integrability of such systems. We provide the normal form for differential systems having an invariant quadric and we study in more detail the dynamics and integrability of quadratic differential systems having an elliptic paraboloid as invariant algebraic surface. Finally, we study the dynamic consequences of perturbing differential system whose phase space is foliated by invariant algebraic surfaces. For this we consider the quadratic differential system known as Sprott A system, which depends on one real parameter a and presents chaotic behavior even without having any equilibrium point, thus having a hidden attractor for suitable values of parameter a. We prove that, for a=0, the phase space of this system is foliated by invariant concentric spheres. By using the Averaging Theory and the KAM (Kolmogorov-Arnold-Moser) Theorem, we prove that, for a>0 sufficiently small, an orbitally stable periodic orbit emerges from a zero-Hopf nonisolated equilibrium point located at the origin and that invariant tori are formed around this periodic orbit. We conclude that the occurrence of these facts has an important role in the formation of the hidden attractor. / FAPESP: 2013/26602-7

Made available in DSpace on 2014-07-29T16:02:20Z (GMT). No. of bitstreams: 1 ALEX NERI GUTIERREZ DISSERTACAO.pdf: 1234288 bytes, checksum: ae65a58b7c2fd793b3c15d44001d82d6 (MD5) Previous issue date: 2012-03-23 / This work has the main objective in the context of the fuzzy theory. Averaging method, differential inclusions are studied; finally this context of the fuzzy theory. / O trabalho tem como objetivo principal, o estudo de um método de averaging em problemas de valor inicial no contexto fuzzy. Com o intuito de facilitar a compreensão do trabalho, faz-se um estudo do, um método de averaging no contexto determinístico, teoria de inclusões diferencias, teoria dos conjuntos fuzzy, inclusões diferenciais fuzzy e finalmente mostra-se o um resultado da validade do método de averaging no contexto fuzzy.

This paper uses Bayesian model comparison methods to simultaneously specify both the spatial weight structure and explanatory variables for a spatial growth regression involving 255 NUTS 2 regions across 25 European countries. In addition, a correct interpretation of the spatial regression parameter estimates that takes into account the simultaneous feed- back nature of the spatial autoregressive model is provided. Our findings indicate that incorporating model uncertainty in conjunction with appropriate parameter interpretation decreased the importance of explanatory variables traditionally thought to exert an important influence on regional income growth rates. (authors' abstract)

Nonlinear limit cycle oscillators are common in nature and man-made equipments, for example, they occur in electronics, robotics, lasers, chemical reactions, biological systems and economical models. Such oscillators demonstrate periodic behavior with fixed frequency and amplitude independently of the system’s initial conditions. The goal of the doctoral thesis is the development and application of phase reduction and averaging methods to analyze particular nonlinear problems in self-oscillatory systems. The phase reduction method allows us to reduce the dynamic of a weakly perturbed limit cycle oscillator to a single scalar equation that defines the dynamics of the phase. This method is usually applied to the systems described by ordinary differential equations. Here this method is extended for the systems with time delay. The phase reduction method is applied to analyze the delayed feedback control (DFC) algorithm. Such an approach allows us to obtain analytical results for slightly mismatched DFC scheme and to stabilize unstable periodic orbits with topological restriction. The averaging method is applied to self-oscillatory systems driven by high-frequency periodic force. The method allows to derive the equations for the slow motion, averaged over high-frequency oscillations. Using this method the mechanism of suppression of sustained neuronal spiking under high frequency electrical stimulation is investigated. / Netiesiniai ribinio ciklo osciliatoriai dažnai sutinkami gamtoje bei žmogaus sukonstruotose sistemose, pavyzdžiui elektronikoje, robototechnikoje, lazeriuose, cheminėse reakcijose, biologinėse sistemose bei ekonominiuose modeliuose. Tokie osciliatoriai vaizduoja periodinį elgesį su fiksuotu dažniu ir amplitude nepriklausomai nuo sistemos pradinių sąlygų. Šios disertacijos tikslas yra išplėtoti ir pritaikyti fazinės redukcijos ir vidurkinimo metodus konkretiems uždaviniams spręsti. Fazinės redukcijos metodas leidžia silpnai perturbuoto ribinio ciklo osciliatoriaus dinamiką redukuoti iki vieno skaliarinio kintamojo dinamikos. Darbe fazinės redukcijos metodas išplėtotas ribinio ciklo osciliatoriams su delsa. Plačiai išnagrinėtas fazinės redukcijos taikymas chaotinėms sistemoms, kurių nestabili periodinė orbita (NPO) yra stabilizuojama uždelstuoju grįžtamuoju ryšiu (UGR). Toks priėjimas leidžia gauti analizinius rezultatus silpnai išderintai URG valdomai sistemai bei stabilizuoti NPO su topologiniu ribojimu. Vidurkinimo metodas leidžia gauti sistemos dinamiką, suvidurkintą per aukšto dažnio periodą, kai sistema yra veikiama aukšto dažnio periodine jėga. Darbe yra išnagrinėtas neuronų savųjų osciliacijų nuslopinimo mechanizmas, stimuliuojant juos aukšto dažnio elektriniu signalu.

Netiesiniai ribinio ciklo osciliatoriai dažnai sutinkami gamtoje bei žmogaus sukonstruotose sistemose, pavyzdžiui elektronikoje, robototechnikoje, lazeriuose, cheminėse reakcijose, biologinėse sistemose bei ekonominiuose modeliuose. Tokie osciliatoriai vaizduoja periodinį elgesį su fiksuotu dažniu ir amplitude nepriklausomai nuo sistemos pradinių sąlygų. Šios disertacijos tikslas yra išplėtoti ir pritaikyti fazinės redukcijos ir vidurkinimo metodus konkretiems uždaviniams spręsti. Fazinės redukcijos metodas leidžia silpnai perturbuoto ribinio ciklo osciliatoriaus dinamiką redukuoti iki vieno skaliarinio kintamojo dinamikos. Darbe fazinės redukcijos metodas išplėtotas ribinio ciklo osciliatoriams su delsa. Plačiai išnagrinėtas fazinės redukcijos taikymas chaotinėms sistemoms, kurių nestabili periodinė orbita (NPO) yra stabilizuojama uždelstuoju grįžtamuoju ryšiu (UGR). Toks priėjimas leidžia gauti analizinius rezultatus silpnai išderintai URG valdomai sistemai bei stabilizuoti NPO su topologiniu ribojimu. Vidurkinimo metodas leidžia gauti sistemos dinamiką, suvidurkintą per aukšto dažnio periodą, kai sistema yra veikiama aukšto dažnio periodine jėga. Darbe yra išnagrinėtas neuronų savųjų osciliacijų nuslopinimo mechanizmas, stimuliuojant juos aukšto dažnio elektriniu signalu. / Nonlinear limit cycle oscillators are common in nature and man-made equipments, for example, they occur in electronics, robotics, lasers, chemical reactions, biological systems and economical models. Such oscillators demonstrate periodic behavior with fixed frequency and amplitude independently of the system’s initial conditions. The goal of the doctoral thesis is the development and application of phase reduction and averaging methods to analyze particular nonlinear problems in self-oscillatory systems. The phase reduction method allows us to reduce the dynamic of a weakly perturbed limit cycle oscillator to a single scalar equation that defines the dynamics of the phase. This method is usually applied to the systems described by ordinary differential equations. Here this method is extended for the systems with time delay. The phase reduction method is applied to analyze the delayed feedback control (DFC) algorithm. Such an approach allows us to obtain analytical results for slightly mismatched DFC scheme and to stabilize unstable periodic orbits with topological restriction. The averaging method is applied to self-oscillatory systems driven by high-frequency periodic force. The method allows to derive the equations for the slow motion, averaged over high-frequency oscillations. Using this method the mechanism of suppression of sustained neuronal spiking under high frequency electrical stimulation is investigated.

Pharmacometric model-based analysis using nonlinear mixed-effects models (NLMEM) has to date mainly been applied to learning activities in drug development. However, such analyses can also serve as the primary analysis in confirmatory studies, which is expected to bring higher power than traditional analysis methods, among other advantages. Because of the high expertise in designing and interpreting confirmatory studies with other types of analyses and because of a number of unresolved uncertainties regarding the magnitude of potential gains and risks, pharmacometric analyses are traditionally not used as primary analysis in confirmatory trials. The aim of this thesis was to address current hurdles hampering the use of pharmacometric model-based analysis in confirmatory settings by developing strategies to increase model compliance to distributional assumptions regarding the residual error, to improve the quantification of parameter uncertainty and to enable model prespecification. A dynamic transform-both-sides approach capable of handling skewed and/or heteroscedastic residuals and a t-distribution approach allowing for symmetric heavy tails were developed and proved relevant tools to increase model compliance to distributional assumptions regarding the residual error. A diagnostic capable of assessing the appropriateness of parameter uncertainty distributions was developed, showing that currently used uncertainty methods such as bootstrap have limitations for NLMEM. A method based on sampling importance resampling (SIR) was thus proposed, which could provide parameter uncertainty in many situations where other methods fail such as with small datasets, highly nonlinear models or meta-analysis. SIR was successfully applied to predict the uncertainty in human plasma concentrations for the antibiotic colistin and its prodrug colistin methanesulfonate based on an interspecies whole-body physiologically based pharmacokinetic model. Lastly, strategies based on model-averaging were proposed to enable full model prespecification and proved to be valid alternatives to standard methodologies for studies assessing the QT prolongation potential of a drug and for phase III trials in rheumatoid arthritis. In conclusion, improved methods for handling residual error, parameter uncertainty and model uncertainty in NLMEM were successfully developed. As confirmatory trials are among the most demanding in terms of patient-participation, cost and time in drug development, allowing (some of) these trials to be analyzed with pharmacometric model-based methods will help improve the safety and efficiency of drug development.

This paper uses Bayesian Model Averaging (BMA) to find robust determinants of economic growth in a new dataset of 255 European regions between 1995 and 2005. The paper finds that income convergence between countries is dominated by the catching-up of regions in new member states in Central and Eastern Europe (CEE), whereas convergence within countries is driven by regions in old EU member states. Regions containing capital cities are growing faster, particularly in CEE countries, as do regions with a large share of workers with higher education. The results are robust to allowing for spatial spillovers among European regions.

Understanding the determinants of aggregated default probabilities (PDs) has attracted substantial research over the past decades. This study addresses two major difficulties in understanding the determinants of aggregate PDs: Model uncertainty and multicollinearity among the regressors. We present Bayesian Model Averaging (BMA) as a powerful tool that overcomes model uncertainty. Furthermore, we supplement BMA with ridge regression to mitigate multicollinearity. We apply our approach to an Austrian dataset. Our findings suggest that factor prices like short term interest rates and energy prices constitute major drivers of default rates, while firms' profits reduce the expected number of failures. Finally, we show that the results of our baseline model are fairly robust to the choice of the prior model size. / Series: Research Report Series / Department of Statistics and Mathematics

La description aux échelles macroscopiques et gigascopiques des feux de forêts permet l'établissement de modèles physiques aptes à représenter l'évolution d'un feu avec une meilleure précision que les modèles empiriques de type Rothermel développés jusqu'alors. Cependant ces modèles nécessitent l'ajustement de paramètres dont la mesure directe est impossible, car les équations associées à ces modèles ne sont pas relatives à l'air et à la matière végétale mais aux milieux équivalents à la végétation pour l'échelle considérée. Les propriétés des milieux équivalents sont alors liées aux propriétés des milieux les constituant, mais la connaissance des propriétés des milieux constitutifs ne permet pas de connaître directement les propriétés du milieu équivalent. Ce travail consistera tout d'abord en la reconstruction du milieu végétal à l'aide d'outils issus de la géométrie fractale. Des méthodes de mesures de paramètres géométriques venant de la foresterie ont ensuite été utilisées pour valider nos modèles de végétation. Enfin, des expériences numériques ont été menées sur nos structures reconstruites afin d'identifier les paramètres macroscopiques qui nous intéressent. Ces expériences permettent également de valider ou non les hypothèses effectuées lors de l'établissement des équations du milieu équivalent. Les paramètres ajustés sont la viscosité du milieu équivalent, le coefficient d'échange convectif et le coefficient d'extinction / The macroscopic and gigascopic scale description of forest fires allows physical modelings of the propagation which can predict the fire evolution with a better accuracy than usually developed empirical Rothermel-like models. However, those models need fitting for their parameters which cannot be measured directly as the models equations are related to the equivalent media at the considered scale and not related to the air and the vegetal material. The equivalent media properties are related to the inner media properties, but the inner media properties knowledge does not allow directly the equivalent media properties knowledge. This work is then aiming on the vegetal medium reconstruction using fractal geometry. Geometrical parameters measurement methods used in forestry sciences are applied for the vegetal modeling validation. Numerical studies are finally done on the reconstructed structures to fit the relevant macroscopic scale parameters. Those studies also allow us to validate or invalidate the assumptions which have been done for the equivalent medium equation development. Those parameters are: the equivalent medium viscosity, the convective heat transfer coefficient and the extinction coefficient