Decision boundary for discrete Bayesian network classifiers

Bayesian network classifiers are a powerful machine learning tool. In order to evaluate the expressive power of these models, we compute families of polynomials that sign-represent decision functions induced by Bayesian network classifiers. We prove that those families are linear combinations of products of Lagrange basis polynomials. In absence of V-structures in the predictor sub-graph, we are also able to prove that this family of polynomials does in- deed characterize the specific classifier considered. We then use this representation to bound the number of decision functions representable by Bayesian network classifiers with a given structure and we compare these bounds to the ones obtained using Vapnik-Chervonenkis dimension.

Application of a Bayesian/Generalised Least-Squares method to generate correlations between independent neutron fission yield data

Fission product yields are fundamental parameters for several nuclear engineering calculations and in particular for burn-up/activation problems. The impact of their uncertainties was widely studied in the past and valuations were released, although still incomplete. Recently, the nuclear community expressed the need for full fission yield covariance matrices to produce inventory calculation results that take into account the complete uncertainty data. In this work, we studied and applied a Bayesian/generalised least-squares method for covariance generation, and compared the generated uncertainties to the original data stored in the JEFF-3.1.2 library. Then, we focused on the effect of fission yield covariance information on fission pulse decay heat results for thermal fission of 235U. Calculations were carried out using different codes (ACAB and ALEPH-2) after introducing the new covariance values. Results were compared with those obtained with the uncertainty data currently provided by the library. The uncertainty quantification was performed with the Monte Carlo sampling technique. Indeed, correlations between fission yields strongly affect the statistics of decay heat. Introduction Nowadays, any engineering calculation performed in the nuclear field should be accompanied by an uncertainty analysis. In such an analysis, different sources of uncertainties are taken into account. Works such as those performed under the UAM project (Ivanov, et al., 2013) treat nuclear data as a source of uncertainty, in particular cross-section data for which uncertainties given in the form of covariance matrices are already provided in the major nuclear data libraries. Meanwhile, fission yield uncertainties were often neglected or treated shallowly, because their effects were considered of second order compared to cross-sections (Garcia-Herranz, et al., 2010). However, the Working Party on International Nuclear Data Evaluation Co-operation (WPEC)

Modelling uncertainty of flood quantile estimation at ungauged sites by Bayesian networks

Prediction at ungauged sites is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. Regression models relate physiographic and climatic basin characteristics to flood quantiles, which can be estimated from observed data at gauged sites. However, these models assume linear relationships between variables Prediction intervals are estimated by the variance of the residuals in the estimated model. Furthermore, the effect of the uncertainties in the explanatory variables on the dependent variable cannot be assessed. This paper presents a methodology to propagate the uncertainties that arise in the process of predicting flood quantiles at ungauged basins by a regression model. In addition, Bayesian networks were explored as a feasible tool for predicting flood quantiles at ungauged sites. Bayesian networks benefit from taking into account uncertainties thanks to their probabilistic nature. They are able to capture non-linear relationships between variables and they give a probability distribution of discharges as result. The methodology was applied to a case study in the Tagus basin in Spain.

On the approximate parametrization problem of algebraic curves.

The problem of parameterizing approximately algebraic curves and surfaces is an active research field, with many implications in practical applications. The problem can be treated locally or globally. We formally state the problem, in its global version for the case of algebraic curves (planar or spatial), and we report on some algorithms approaching it, as well as on the associated error distance analysis.

Computation of nonlinear streaky structures in boundary layer flow

In this work, the Reduced Navier Stokes (RNS) are numerically integrated, and used to calculate nonlinear finite amplitude streaks. These structures are interesting since they can have a stabilizing effect and delay the transition to the turbulent regime. RNS formulation is also used to compute the family of nonlinear intrinsic streaks that emerge from the leading edge in absence of any external perturbation. Finally, this formulation is generalized to include the possibility of having a curved bottom wall

Adaptable Bayesian classifier for spatiotemporal nonparametric moving object detection strategies

Electronic devices endowed with camera platforms require new and powerful machine vision applications, which commonly include moving object detection strategies. To obtain high-quality results, the most recent strategies estimate nonparametrically background and foreground models and combine them by means of a Bayesian classifier. However, typical classifiers are limited by the use of constant prior values and they do not allow the inclusion of additional spatiodependent prior information. In this Letter, we propose an alternative Bayesian classifier that, unlike those reported before, allows the use of additional prior information obtained from any source and depending on the spatial position of each pixel.

PIC computation of electron current collection to a moving bare tether in the mesothermal condition

In tethered satellite technology, it is important to estimate how many electrons a spacecraft can collect from its ambient plasma by a bare electrodynamic tether. The analysis is however very difficult because of the small but significant Geo-magnetic field and the spacecraft’s relative motion to both ions and electrons. The object of our work is the development of a numerical method, for this purpose. Particle-In-Cell (PIC) method, for the calculation of electron current to a positive bare tether moving at orbital velocity in the ionosphere, i.e. in a flowing magnetized plasma under Maxwellian collisionless conditions. In a PIC code, a number of particles are distributed in phase space and the computational domain has a grid on which Poisson equation is solved for field quantities. The code uses the quasi-neutrality condition to solve for the local potential at points in the plasma which coincide with the computational outside boundary. The quasi-neutrality condition imposes ne - ni on the boundary. The Poisson equation is solved in such a way that the presheath region can be captured in the computation. Results show that the collected current is higher than the Orbital Motion Limit (OML) theory. The OML current is the upper limit of current collection under steady collisionless unmagnetized conditions. In this work, we focus on the flowing effects of plasma as a possible cause of the current enhancement. A deficit electron density due to the flowing effects has been worked and removed by introducing adiabatic electron trapping into our model.

Decision boundary for discrete Bayesian network classifiers

Bayesian network classifiers are a powerful machine learning tool. In order to evaluate the expressive power of these models, we compute families of polynomials that sign-represent decision functions induced by Bayesian network classifiers. We prove that those families are linear combinations of products of Lagrange basis polynomials. In absence of V-structures in the predictor sub-graph, we are also able to prove that this family of polynomials does in- deed characterize the specific classifier considered. We then use this representation to bound the number of decision functions representable by Bayesian network classifiers with a given structure and we compare these bounds to the ones obtained using Vapnik-Chervonenkis dimension.

Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.

Regression models with MoPs Bayesian networks

We present a model of Bayesian network for continuous variables, where densities and conditional densities are estimated with B-spline MoPs. We use a novel approach to directly obtain conditional densities estimation using B-spline properties. In particular we implement naive Bayes and wrapper variables selection. Finally we apply our techniques to the problem of predicting neurons morphological variables from electrophysiological ones.

Novel techniques for automorphism group computation

Graph automorphism (GA) is a classical problem, in which the objective is to compute the automorphism group of an input graph. In this work we propose four novel techniques to speed up algorithms that solve the GA problem by exploring a search tree. They increase the performance of the algorithm by allowing to reduce the depth of the search tree, and by effectively pruning it. We formally prove that a GA algorithm that uses these techniques correctly computes the automorphism group of the input graph. We also describe how the techniques have been incorporated into the GA algorithm conauto, as conauto-2.03, with at most an additive polynomial increase in its asymptotic time complexity. We have experimentally evaluated the impact of each of the above techniques with several graph families. We have observed that each of the techniques by itself significantly reduces the number of processed nodes of the search tree in some subset of graphs, which justifies the use of each of them. Then, when they are applied together, their effect is combined, leading to reductions in the number of processed nodes in most graphs. This is also reflected in a reduction of the running time, which is substantial in some graph families.

Bayesian model selection methodology for road safety

Road accidents are a very relevant issue in many countries and macroeconomic models are very frequently applied by academia and administrations to reduce their frequency and consequences. The selection of explanatory variables and response transformation parameter within the Bayesian framework for the selection of the set of explanatory variables a TIM and 3IM (two input and three input models) procedures are proposed. The procedure also uses the DIC and pseudo -R2 goodness of fit criteria. The model to which the methodology is applied is a dynamic regression model with Box-Cox transformation (BCT) for the explanatory variables and autorgressive (AR) structure for the response. The initial set of 22 explanatory variables are identified. The effects of these factors on the fatal accident frequency in Spain, during 2000-2012, are estimated. The dependent variable is constructed considering the stochastic trend component.

Bayesian model selection of structural explanatory models.

In this study we are proposing a Bayesian model selection methodology, where the best model from the list of candidate structural explanatory models is selected. The model structure is based on the Zellner's (1971)explanatory model with autoregressive errors. For the selection technique we are using a parsimonious model, where the model variables are transformed using Box and Cox (1964) class of transformations.

Bayesian model selection of structural explanatory models: Application to road accident data

Using the Bayesian approach as the model selection criteria, the main purpose in this study is to establish a practical road accident model that can provide a better interpretation and prediction performance. For this purpose we are using a structural explanatory model with autoregressive error term. The model estimation is carried out through Bayesian inference and the best model is selected based on the goodness of fit measures. To cross validate the model estimation further prediction analysis were done. As the road safety measures the number of fatal accidents in Spain, during 2000-2011 were employed. The results of the variable selection process show that the factors explaining fatal road accidents are mainly exposure, economic factors, and surveillance and legislative measures. The model selection shows that the impact of economic factors on fatal accidents during the period under study has been higher compared to surveillance and legislative measures.

Contribuciones al análisis de problemas supercomplejos de toma de decisiones

Los fundamentos de la Teoría de la Decisión Bayesiana proporcionan un marco coherente en el que se pueden resolver los problemas de toma de decisiones. La creciente disponibilidad de ordenadores potentes está llevando a tratar problemas cada vez más complejos con numerosas fuentes de incertidumbre multidimensionales; varios objetivos conflictivos; preferencias, metas y creencias cambiantes en el tiempo y distintos grupos afectados por las decisiones. Estos factores, a su vez, exigen mejores herramientas de representación de problemas; imponen fuertes restricciones cognitivas sobre los decisores y conllevan difíciles problemas computacionales. Esta tesis tratará estos tres aspectos. En el Capítulo 1, proporcionamos una revisión crítica de los principales métodos gráficos de representación y resolución de problemas, concluyendo con algunas recomendaciones fundamentales y generalizaciones. Nuestro segundo comentario nos lleva a estudiar tales métodos cuando sólo disponemos de información parcial sobre las preferencias y creencias del decisor. En el Capítulo 2, estudiamos este problema cuando empleamos diagramas de influencia (DI). Damos un algoritmo para calcular las soluciones no dominadas en un DI y analizamos varios conceptos de solución ad hoc. El último aspecto se estudia en los Capítulos 3 y 4. Motivado por una aplicación de gestión de embalses, introducimos un método heurístico para resolver problemas de decisión secuenciales. Como muestra resultados muy buenos, extendemos la idea a problemas secuenciales generales y cuantificamos su bondad. Exploramos después en varias direcciones la aplicación de métodos de simulación al Análisis de Decisiones. Introducimos primero métodos de Monte Cario para aproximar el conjunto no dominado en problemas continuos. Después, proporcionamos un método de Monte Cario basado en cadenas de Markov para problemas con información completa con estructura general: las decisiones y las variables aleatorias pueden ser continuas, y la función de utilidad puede ser arbitraria. Nuestro esquema es aplicable a muchos problemas modelizados como DI. Finalizamos con un capítulo de conclusiones y problemas abiertos.---ABSTRACT---The foundations of Bayesian Decisión Theory provide a coherent framework in which decisión making problems may be solved. With the advent of powerful computers and given the many challenging problems we face, we are gradually attempting to solve more and more complex decisión making problems with high and multidimensional uncertainty, múltiple objectives, influence of time over decisión tasks and influence over many groups. These complexity factors demand better representation tools for decisión making problems; place strong cognitive demands on the decison maker judgements; and lead to involved computational problems. This thesis will deal with these three topics. In recent years, many representation tools have been developed for decisión making problems. In Chapter 1, we provide a critical review of most of them and conclude with recommendations and generalisations. Given our second query, we could wonder how may we deal with those representation tools when there is only partial information. In Chapter 2, we find out how to deal with such a problem when it is structured as an influence diagram (ID). We give an algorithm to compute nondominated solutions in ID's and analyse several ad hoc solution concepts.- The last issue is studied in Chapters 3 and 4. In a reservoir management case study, we have introduced a heuristic method for solving sequential decisión making problems. Since it shows very good performance, we extend the idea to general problems and quantify its goodness. We explore then in several directions the application of simulation based methods to Decisión Analysis. We first introduce Monte Cario methods to approximate the nondominated set in continuous problems. Then, we provide a Monte Cario Markov Chain method for problems under total information with general structure: decisions and random variables may be continuous, and the utility function may be arbitrary. Our scheme is applicable to many problems modeled as IDs. We conclude with discussions and several open problems.