Contributions to Bayesian network learning with applications to neuroscience

Neuronal morphology is a key feature in the study of brain circuits, as it is highly related to information processing and functional identification. Neuronal morphology affects the process of integration of inputs from other neurons and determines the neurons which receive the output of the neurons. Different parts of the neurons can operate semi-independently according to the spatial location of the synaptic connections. As a result, there is considerable interest in the analysis of the microanatomy of nervous cells since it constitutes an excellent tool for better understanding cortical function. However, the morphologies, molecular features and electrophysiological properties of neuronal cells are extremely variable. Except for some special cases, this variability makes it hard to find a set of features that unambiguously define a neuronal type. In addition, there are distinct types of neurons in particular regions of the brain. This morphological variability makes the analysis and modeling of neuronal morphology a challenge. Uncertainty is a key feature in many complex real-world problems. Probability theory provides a framework for modeling and reasoning with uncertainty. Probabilistic graphical models combine statistical theory and graph theory to provide a tool for managing domains with uncertainty. In particular, we focus on Bayesian networks, the most commonly used probabilistic graphical model. In this dissertation, we design new methods for learning Bayesian networks and apply them to the problem of modeling and analyzing morphological data from neurons. The morphology of a neuron can be quantified using a number of measurements, e.g., the length of the dendrites and the axon, the number of bifurcations, the direction of the dendrites and the axon, etc. These measurements can be modeled as discrete or continuous data. The continuous data can be linear (e.g., the length or the width of a dendrite) or directional (e.g., the direction of the axon). These data may follow complex probability distributions and may not fit any known parametric distribution. Modeling this kind of problems using hybrid Bayesian networks with discrete, linear and directional variables poses a number of challenges regarding learning from data, inference, etc. In this dissertation, we propose a method for modeling and simulating basal dendritic trees from pyramidal neurons using Bayesian networks to capture the interactions between the variables in the problem domain. A complete set of variables is measured from the dendrites, and a learning algorithm is applied to find the structure and estimate the parameters of the probability distributions included in the Bayesian networks. Then, a simulation algorithm is used to build the virtual dendrites by sampling values from the Bayesian networks, and a thorough evaluation is performed to show the model’s ability to generate realistic dendrites. In this first approach, the variables are discretized so that discrete Bayesian networks can be learned and simulated. Then, we address the problem of learning hybrid Bayesian networks with different kinds of variables. Mixtures of polynomials have been proposed as a way of representing probability densities in hybrid Bayesian networks. We present a method for learning mixtures of polynomials approximations of one-dimensional, multidimensional and conditional probability densities from data. The method is based on basis spline interpolation, where a density is approximated as a linear combination of basis splines. The proposed algorithms are evaluated using artificial datasets. We also use the proposed methods as a non-parametric density estimation technique in Bayesian network classifiers. Next, we address the problem of including directional data in Bayesian networks. These data have some special properties that rule out the use of classical statistics. Therefore, different distributions and statistics, such as the univariate von Mises and the multivariate von Mises–Fisher distributions, should be used to deal with this kind of information. In particular, we extend the naive Bayes classifier to the case where the conditional probability distributions of the predictive variables given the class follow either of these distributions. We consider the simple scenario, where only directional predictive variables are used, and the hybrid case, where discrete, Gaussian and directional distributions are mixed. The classifier decision functions and their decision surfaces are studied at length. Artificial examples are used to illustrate the behavior of the classifiers. The proposed classifiers are empirically evaluated over real datasets. We also study the problem of interneuron classification. An extensive group of experts is asked to classify a set of neurons according to their most prominent anatomical features. A web application is developed to retrieve the experts’ classifications. We compute agreement measures to analyze the consensus between the experts when classifying the neurons. Using Bayesian networks and clustering algorithms on the resulting data, we investigate the suitability of the anatomical terms and neuron types commonly used in the literature. Additionally, we apply supervised learning approaches to automatically classify interneurons using the values of their morphological measurements. Then, a methodology for building a model which captures the opinions of all the experts is presented. First, one Bayesian network is learned for each expert, and we propose an algorithm for clustering Bayesian networks corresponding to experts with similar behaviors. Then, a Bayesian network which represents the opinions of each group of experts is induced. Finally, a consensus Bayesian multinet which models the opinions of the whole group of experts is built. A thorough analysis of the consensus model identifies different behaviors between the experts when classifying the interneurons in the experiment. A set of characterizing morphological traits for the neuronal types can be defined by performing inference in the Bayesian multinet. These findings are used to validate the model and to gain some insights into neuron morphology. Finally, we study a classification problem where the true class label of the training instances is not known. Instead, a set of class labels is available for each instance. This is inspired by the neuron classification problem, where a group of experts is asked to individually provide a class label for each instance. We propose a novel approach for learning Bayesian networks using count vectors which represent the number of experts who selected each class label for each instance. These Bayesian networks are evaluated using artificial datasets from supervised learning problems. Resumen La morfología neuronal es una característica clave en el estudio de los circuitos cerebrales, ya que está altamente relacionada con el procesado de información y con los roles funcionales. La morfología neuronal afecta al proceso de integración de las señales de entrada y determina las neuronas que reciben las salidas de otras neuronas. Las diferentes partes de la neurona pueden operar de forma semi-independiente de acuerdo a la localización espacial de las conexiones sinápticas. Por tanto, existe un interés considerable en el análisis de la microanatomía de las células nerviosas, ya que constituye una excelente herramienta para comprender mejor el funcionamiento de la corteza cerebral. Sin embargo, las propiedades morfológicas, moleculares y electrofisiológicas de las células neuronales son extremadamente variables. Excepto en algunos casos especiales, esta variabilidad morfológica dificulta la definición de un conjunto de características que distingan claramente un tipo neuronal. Además, existen diferentes tipos de neuronas en regiones particulares del cerebro. La variabilidad neuronal hace que el análisis y el modelado de la morfología neuronal sean un importante reto científico. La incertidumbre es una propiedad clave en muchos problemas reales. La teoría de la probabilidad proporciona un marco para modelar y razonar bajo incertidumbre. Los modelos gráficos probabilísticos combinan la teoría estadística y la teoría de grafos con el objetivo de proporcionar una herramienta con la que trabajar bajo incertidumbre. En particular, nos centraremos en las redes bayesianas, el modelo más utilizado dentro de los modelos gráficos probabilísticos. En esta tesis hemos diseñado nuevos métodos para aprender redes bayesianas, inspirados por y aplicados al problema del modelado y análisis de datos morfológicos de neuronas. La morfología de una neurona puede ser cuantificada usando una serie de medidas, por ejemplo, la longitud de las dendritas y el axón, el número de bifurcaciones, la dirección de las dendritas y el axón, etc. Estas medidas pueden ser modeladas como datos continuos o discretos. A su vez, los datos continuos pueden ser lineales (por ejemplo, la longitud o la anchura de una dendrita) o direccionales (por ejemplo, la dirección del axón). Estos datos pueden llegar a seguir distribuciones de probabilidad muy complejas y pueden no ajustarse a ninguna distribución paramétrica conocida. El modelado de este tipo de problemas con redes bayesianas híbridas incluyendo variables discretas, lineales y direccionales presenta una serie de retos en relación al aprendizaje a partir de datos, la inferencia, etc. En esta tesis se propone un método para modelar y simular árboles dendríticos basales de neuronas piramidales usando redes bayesianas para capturar las interacciones entre las variables del problema. Para ello, se mide un amplio conjunto de variables de las dendritas y se aplica un algoritmo de aprendizaje con el que se aprende la estructura y se estiman los parámetros de las distribuciones de probabilidad que constituyen las redes bayesianas. Después, se usa un algoritmo de simulación para construir dendritas virtuales mediante el muestreo de valores de las redes bayesianas. Finalmente, se lleva a cabo una profunda evaluaci ón para verificar la capacidad del modelo a la hora de generar dendritas realistas. En esta primera aproximación, las variables fueron discretizadas para poder aprender y muestrear las redes bayesianas. A continuación, se aborda el problema del aprendizaje de redes bayesianas con diferentes tipos de variables. Las mixturas de polinomios constituyen un método para representar densidades de probabilidad en redes bayesianas híbridas. Presentamos un método para aprender aproximaciones de densidades unidimensionales, multidimensionales y condicionales a partir de datos utilizando mixturas de polinomios. El método se basa en interpolación con splines, que aproxima una densidad como una combinación lineal de splines. Los algoritmos propuestos se evalúan utilizando bases de datos artificiales. Además, las mixturas de polinomios son utilizadas como un método no paramétrico de estimación de densidades para clasificadores basados en redes bayesianas. Después, se estudia el problema de incluir información direccional en redes bayesianas. Este tipo de datos presenta una serie de características especiales que impiden el uso de las técnicas estadísticas clásicas. Por ello, para manejar este tipo de información se deben usar estadísticos y distribuciones de probabilidad específicos, como la distribución univariante von Mises y la distribución multivariante von Mises–Fisher. En concreto, en esta tesis extendemos el clasificador naive Bayes al caso en el que las distribuciones de probabilidad condicionada de las variables predictoras dada la clase siguen alguna de estas distribuciones. Se estudia el caso base, en el que sólo se utilizan variables direccionales, y el caso híbrido, en el que variables discretas, lineales y direccionales aparecen mezcladas. También se estudian los clasificadores desde un punto de vista teórico, derivando sus funciones de decisión y las superficies de decisión asociadas. El comportamiento de los clasificadores se ilustra utilizando bases de datos artificiales. Además, los clasificadores son evaluados empíricamente utilizando bases de datos reales. También se estudia el problema de la clasificación de interneuronas. Desarrollamos una aplicación web que permite a un grupo de expertos clasificar un conjunto de neuronas de acuerdo a sus características morfológicas más destacadas. Se utilizan medidas de concordancia para analizar el consenso entre los expertos a la hora de clasificar las neuronas. Se investiga la idoneidad de los términos anatómicos y de los tipos neuronales utilizados frecuentemente en la literatura a través del análisis de redes bayesianas y la aplicación de algoritmos de clustering. Además, se aplican técnicas de aprendizaje supervisado con el objetivo de clasificar de forma automática las interneuronas a partir de sus valores morfológicos. A continuación, se presenta una metodología para construir un modelo que captura las opiniones de todos los expertos. Primero, se genera una red bayesiana para cada experto y se propone un algoritmo para agrupar las redes bayesianas que se corresponden con expertos con comportamientos similares. Después, se induce una red bayesiana que modela la opinión de cada grupo de expertos. Por último, se construye una multired bayesiana que modela las opiniones del conjunto completo de expertos. El análisis del modelo consensuado permite identificar diferentes comportamientos entre los expertos a la hora de clasificar las neuronas. Además, permite extraer un conjunto de características morfológicas relevantes para cada uno de los tipos neuronales mediante inferencia con la multired bayesiana. Estos descubrimientos se utilizan para validar el modelo y constituyen información relevante acerca de la morfología neuronal. Por último, se estudia un problema de clasificación en el que la etiqueta de clase de los datos de entrenamiento es incierta. En cambio, disponemos de un conjunto de etiquetas para cada instancia. Este problema está inspirado en el problema de la clasificación de neuronas, en el que un grupo de expertos proporciona una etiqueta de clase para cada instancia de manera individual. Se propone un método para aprender redes bayesianas utilizando vectores de cuentas, que representan el número de expertos que seleccionan cada etiqueta de clase para cada instancia. Estas redes bayesianas se evalúan utilizando bases de datos artificiales de problemas de aprendizaje supervisado.

Learning an L1-regularized Gaussian Bayesian Network in the Equivalence Class Space

Learning the structure of a graphical model from data is a common task in a wide range of practical applications. In this paper, we focus on Gaussian Bayesian networks, i.e., on continuous data and directed acyclic graphs with a joint probability density of all variables given by a Gaussian. We propose to work in an equivalence class search space, specifically using the k-greedy equivalence search algorithm. This, combined with regularization techniques to guide the structure search, can learn sparse networks close to the one that generated the data. We provide results on some synthetic networks and on modeling the gene network of the two biological pathways regulating the biosynthesis of isoprenoids for the Arabidopsis thaliana plant

Markov blanket-based approach for learning multi-dimensional Bayesian network classifiers: An application to predict the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson's Disease Questionnaire (PDQ-39)

Multi-dimensional Bayesian network classifiers (MBCs) are probabilistic graphical models recently proposed to deal with multi-dimensional classification problems, where each instance in the data set has to be assigned to more than one class variable. In this paper, we propose a Markov blanket-based approach for learning MBCs from data. Basically, it consists of determining the Markov blanket around each class variable using the HITON algorithm, then specifying the directionality over the MBC subgraphs. Our approach is applied to the prediction problem of the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson’s Disease Questionnaire (PDQ-39) in order to estimate the health-related quality of life of Parkinson’s patients. Fivefold cross-validation experiments were carried out on randomly generated synthetic data sets, Yeast data set, as well as on a real-world Parkinson’s disease data set containing 488 patients. The experimental study, including comparison with additional Bayesian network-based approaches, back propagation for multi-label learning, multi-label k-nearest neighbor, multinomial logistic regression, ordinary least squares, and censored least absolute deviations, shows encouraging results in terms of predictive accuracy as well as the identification of dependence relationships among class and feature variables.

Learning Bayesian networks from data by the incremental compilation of new network polynomials

Probabilistic graphical models are a huge research field in artificial intelligence nowadays. The scope of this work is the study of directed graphical models for the representation of discrete distributions. Two of the main research topics related to this area focus on performing inference over graphical models and on learning graphical models from data. Traditionally, the inference process and the learning process have been treated separately, but given that the learned models structure marks the inference complexity, this kind of strategies will sometimes produce very inefficient models. With the purpose of learning thinner models, in this master thesis we propose a new model for the representation of network polynomials, which we call polynomial trees. Polynomial trees are a complementary representation for Bayesian networks that allows an efficient evaluation of the inference complexity and provides a framework for exact inference. We also propose a set of methods for the incremental compilation of polynomial trees and an algorithm for learning polynomial trees from data using a greedy score+search method that includes the inference complexity as a penalization in the scoring function.

Exploring three approaches to offer distance learning courses through a social network of health researchers in three African countries

The Institute of Tropical Medicine in Antwerp hereby presents the results of two pilot distance learning training programmes, developed under the umbrella of the AFRICA BUILD project (FP7). The two courses focused on evidence-based medicine (EBM): with the aim of enhancing research and education, via novel approaches and to identify research needs emanating from the field. These pilot experiences, which were run both in English-speaking (Ghana), and French-speaking (Mali and Cameroon) partner institutions, produced targeted courses for the strengthening of research methodology and policy. The courses and related study materials are in the public domain and available through the AFRICA BUILD Portal (http://www.africabuild.eu/taxonomy/term/37); the training modules were delivered live via Dudal webcasts. This paper assesses the success and difficulties of transferring EBM skills with these two specific training programmes, offered through three different approaches: fully online facultative courses, fully online tutor supported courses or through a blended approach with both online and face-to-face sessions. Key factors affecting the selection of participants, the accessibility of the courses, how the learning resources are offered, and how interactive online communities are formed, are evaluated and discussed.

Co-evolutionary and Reinforcement Learning Techniques Applied to Computer Go players

The objective of this thesis is model some processes from the nature as evolution and co-evolution, and proposing some techniques that can ensure that these learning process really happens and useful to solve some complex problems as Go game. The Go game is ancient and very complex game with simple rules which still is a challenge for the Artificial Intelligence. This dissertation cover some approaches that were applied to solve this problem, proposing solve this problem using competitive and cooperative co-evolutionary learning methods and other techniques proposed by the author. To study, implement and prove these methods were used some neural networks structures, a framework free available and coded many programs. The techniques proposed were coded by the author, performed many experiments to find the best configuration to ensure that co-evolution is progressing and discussed the results. Using co-evolutionary learning processes can be observed some pathologies which could impact co-evolution progress. In this dissertation is introduced some techniques to solve pathologies as loss of gradients, cycling dynamics and forgetting. According to some authors, one solution to solve these co-evolution pathologies is introduce more diversity in populations that are evolving. In this thesis is proposed some techniques to introduce more diversity and some diversity measurements for neural networks structures to monitor diversity during co-evolution. The genotype diversity evolved were analyzed in terms of its impact to global fitness of the strategies evolved and their generalization. Additionally, it was introduced a memory mechanism in the network neural structures to reinforce some strategies in the genes of the neurons evolved with the intention that some good strategies learned are not forgotten. In this dissertation is presented some works from other authors in which cooperative and competitive co-evolution has been applied. The Go board size used in this thesis was 9x9, but can be easily escalated to more bigger boards.The author believe that programs coded and techniques introduced in this dissertation can be used for other domains.

TELMA: Technology enhanced learning environment for minimally invasive surgery

Background: Cognitive skills training for minimally invasive surgery has traditionally relied upon diverse tools, such as seminars or lectures. Web technologies for e-learning have been adopted to provide ubiquitous training and serve as structured repositories for the vast amount of laparoscopic video sources available. However, these technologies fail to offer such features as formative and summative evaluation, guided learning, or collaborative interaction between users. Methodology: The "TELMA" environment is presented as a new technology-enhanced learning platform that increases the user's experience using a four-pillared architecture: (1) an authoring tool for the creation of didactic contents; (2) a learning content and knowledge management system that incorporates a modular and scalable system to capture, catalogue, search, and retrieve multimedia content; (3) an evaluation module that provides learning feedback to users; and (4) a professional network for collaborative learning between users. Face validation of the environment and the authoring tool are presented. Results: Face validation of TELMA reveals the positive perception of surgeons regarding the implementation of TELMA and their willingness to use it as a cognitive skills training tool. Preliminary validation data also reflect the importance of providing an easy-to-use, functional authoring tool to create didactic content. Conclusion: The TELMA environment is currently installed and used at the Jesús Usón Minimally Invasive Surgery Centre and several other Spanish hospitals. Face validation results ascertain the acceptance and usefulness of this new minimally invasive surgery training environment.

Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods.

E-MIS validity applied to TELMA enhanced learning environment

Enhanced learning environments are arising with great success within the field of cognitive skills training in minimally invasive surgery (MIS) because they provides multiple benefits since they avoid time, spatial and cost constraints. TELMA [1,2] is a new technology enhanced learning platform that promotes collaborative and ubiquitous training of surgeons. This platform is based on four main modules: an authoring tool, a learning content and knowledge management system, an evaluation module and a professional network. TELMA has been designed and developed focused on the user; therefore it is necessary to carry out a user validation as final stage of the development. For this purpose, e-MIS validity [3] has been defined. This validation includes usability, contents and functionality validities both for the development and production stages of any e-Learning web platform. Using e-MIS validity, the e-Learning is fully validated since it includes subjective and objective metrics. The purpose of this study is to specify and apply a set of objective and subjective metrics using e-MIS validity to test usability, contents and functionality of TELMA environment within the development stage.

Traditional education vs modern education. What is the impact of teaching techniques' evolution on students learning process?

The main objective of this article is to focus on the analysis of teaching techniques, ranging from the use of the blackboard and chalk in old traditional classes, using slides and overhead projectors in the eighties and use of presentation software in the nineties, to the video, electronic board and network resources nowadays. Furthermore, all the aforementioned, is viewed under the different mentalities in which the teacher conditions the student using the new teaching technique, improving soft skills but maybe leading either to encouragement or disinterest, and including the lack of educational knowledge consolidation at scientific, technology and specific levels. In the same way, we study the process of adaptation required for teachers, the differences in the processes of information transfer and education towards the student, and even the existence of teachers who are not any longer appealed by their work due which has become much simpler due to new technologies and the greater ease in the development of classes due to the criteria described on the new Grade Programs adopted by the European Higher Education Area. Moreover, it is also intended to understand the evolution of students’ profiles, from the eighties to present time, in order to understand certain attitudes, behaviours, accomplishments and acknowledgements acquired over the semesters within the degree Programs. As an Educational Innovation Group, another key question also arises. What will be the learning techniques in the future?. How these evolving matters will affect both positively and negatively on the mentality, attitude, behaviour, learning, achievement of goals and satisfaction levels of all elements involved in universities’ education? Clearly, this evolution from chalk to the electronic board, the three-dimensional view of our works and their sequence, greatly facilitates the understanding and adaptation later on to the business world, but does not answer to the unknowns regarding the knowledge and the full development of achievement’s indicators in basic skills of a degree. This is the underlying question which steers the roots of the presented research.

Incorporating proactivity to context-aware recommender systems for e-learning

Recommender systems in e-learning have proved to be powerful tools to find suitable educational material during the learning experience. But traditional user request-response patterns are still being used to generate these recommendations. By including contextual information derived from the use of ubiquitous learning environments, the possibility of incorporating proactivity to the recommendation process has arisen. In this paper we describe methods to push proactive recommendations to e-learning systems users when the situation is appropriate without being needed their explicit request. As a result, interesting learning objects can be recommended attending to the user?s needs in every situation. The impact of this proactive recommendations generated have been evaluated among teachers and scientists in a real e-learning social network called Virtual Science Hub related to the GLOBAL excursion European project. Outcomes indicate that the methods proposed are valid to generate such kind of recommendations in e-learning scenarios. The results also show that the users' perceived appropriateness of having proactive recommendations is high.

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.

AFRICA BUILD Portal: developing a social network of African health researchers and educators

One of the main outputs of the project is a collaborative platform which integrates a myriad of research and learning resources. This article presents the first prototype of this platform: the AFRICA BUILD Portal (ABP 1.0). The ABP is a Web 2.0 platform which facilitates the access, in a collaborative manner, to these resources. Through a usable web interface, the ABP has been designed to avoid, as much as possible, the connectivity problems of African institutions. In this paper, we suggest that the access to complex systems does not imply slow response rates, and that their development model guides the project to a natural technological transfer, adaptation and user acceptance. Finally, this platform aims to motivate research attitudes during the learning process and stimulate user?s collaborations.

PUE attack detection in CWSN using collaboration and learning behavior

Cognitive Wireless Sensor Network (CWSN) is a new paradigm which integrates cognitive features in traditional Wireless Sensor Networks (WSNs) to mitigate important problems such as spectrum occupancy. Security in Cognitive Wireless Sensor Networks is an important problem because these kinds of networks manage critical applications and data. Moreover, the specific constraints of WSN make the problem even more critical. However, effective solutions have not been implemented yet. Among the specific attacks derived from new cognitive features, the one most studied is the Primary User Emulation (PUE) attack. This paper discusses a new approach, based on anomaly behavior detection and collaboration, to detect the PUE attack in CWSN scenarios. A nonparametric CUSUM algorithm, suitable for low resource networks like CWSN, has been used in this work. The algorithm has been tested using a cognitive simulator that brings important results in this area. For example, the result shows that the number of collaborative nodes is the most important parameter in order to improve the PUE attack detection rates. If the 20% of the nodes collaborates, the PUE detection reaches the 98% with less than 1% of false positives.

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.