Metodologías de modelado, monitorización y asistencia robótica en neurorrehabilitación funcional de extremidad superior

La Organización Mundial de la Salud (OMS) prevé que para el año 2020, el Daño Cerebral Adquirido (DCA) estará entre las 10 causas más comunes de discapacidad. Estas lesiones, dadas sus consecuencias físicas, sensoriales, cognitivas, emocionales y socioeconómicas, cambian dramáticamente la vida de los pacientes y sus familias. Las nuevas técnicas de intervención precoz y el desarrollo de la medicina intensiva en la atención al DCA han mejorado notablemente la probabilidad de supervivencia. Sin embargo, hoy por hoy, las lesiones cerebrales no tienen ningún tratamiento quirúrgico que tenga por objetivo restablecer la funcionalidad perdida, sino que las terapias rehabilitadoras se dirigen hacia la compensación de los déficits producidos. Uno de los objetivos principales de la neurorrehabilitación es, por tanto, dotar al paciente de la capacidad necesaria para ejecutar las Actividades de Vida Diaria (AVDs) necesarias para desarrollar una vida independiente, siendo fundamentales aquellas en las que la Extremidad Superior (ES) está directamente implicada, dada su gran importancia a la hora de la manipulación de objetos. Con la incorporación de nuevas soluciones tecnológicas al proceso de neurorrehabilitación se pretende alcanzar un nuevo paradigma centrado en ofrecer una práctica personalizada, monitorizada y ubicua con una valoración continua de la eficacia y de la eficiencia de los procedimientos y con capacidad de generar conocimientos que impulsen la ruptura del paradigma de actual. Los nuevos objetivos consistirán en minimizar el impacto de las enfermedades que afectan a la capacidad funcional de las personas, disminuir el tiempo de incapacidad y permitir una gestión más eficiente de los recursos. Estos objetivos clínicos, de gran impacto socio-económico, sólo pueden alcanzarse desde una apuesta decidida en nuevas tecnologías, metodologías y algoritmos capaces de ocasionar la ruptura tecnológica necesaria que permita superar las barreras que hasta el momento han impedido la penetración tecnológica en el campo de la rehabilitación de manera universal. De esta forma, los trabajos y resultados alcanzados en la Tesis son los siguientes: 1. Modelado de AVDs: como paso previo a la incorporación de ayudas tecnológicas al proceso rehabilitador, se hace necesaria una primera fase de modelado y formalización del conocimiento asociado a la ejecución de las actividades que se realizan como parte de la terapia. En particular, las tareas más complejas y a su vez con mayor repercusión terapéutica son las AVDs, cuya formalización permitirá disponer de modelos de movimiento sanos que actuarán de referencia para futuros desarrollos tecnológicos dirigidos a personas con DCA. Siguiendo una metodología basada en diagramas de estados UML se han modelado las AVDs 'servir agua de una jarra' y 'coger un botella' 2. Monitorización ubícua del movimiento de la ES: se ha diseñado, desarrollado y validado un sistema de adquisición de movimiento basado en tecnología inercial que mejora las limitaciones de los dispositivos comerciales actuales (coste muy elevado e incapacidad para trabajar en entornos no controlados); los altos coeficientes de correlación y los bajos niveles de error obtenidos en los corregistros llevados a cabo con el sistema comercial BTS SMART-D demuestran la alta precisión del sistema. También se ha realizado un trabajo de investigación exploratorio de un sistema de captura de movimiento de coste muy reducido basado en visión estereoscópica, habiéndose detectado los puntos clave donde se hace necesario incidir desde un punto de vista tecnológico para su incorporación en un entorno real 3. Resolución del Problema Cinemático Inverso (PCI): se ha diseñado, desarrollado y validado una solución al PCI cuando el manipulador se corresponde con una ES humana estudiándose 2 posibles alternativas, una basada en la utilización de un Perceptrón Multicapa (PMC) y otra basada en sistemas Artificial Neuro-Fuzzy Inference Systems (ANFIS). La validación, llevada a cabo utilizando información relativa a los modelos disponibles de AVDs, indica que una solución basada en un PMC con 3 neuronas en la capa de entrada, una capa oculta también de 3 neuronas y una capa de salida con tantas neuronas como Grados de Libertad (GdLs) tenga el modelo de la ES, proporciona resultados, tanto de precisión como de tiempo de cálculo, que la hacen idónea para trabajar en sistemas con requisitos de tiempo real 4. Control inteligente assisted-as-needed: se ha diseñado, desarrollado y validado un algoritmo de control assisted-as-needed para una ortesis robótica con capacidades de actuación anticipatoria de la que existe un prototipo implementado en la actualidad. Los resultados obtenidos demuestran cómo el sistema es capaz de adaptarse al perfil disfuncional del paciente activando la ayuda en instantes anteriores a la ocurrencia de movimientos incorrectos. Esta estrategia implica un aumento en la participación del paciente y, por tanto, en su actividad muscular, fomentándose los procesos la plasticidad cerebral responsables del reaprendizaje o readaptación motora 5. Simuladores robóticos para planificación: se propone la utilización de un simulador robótico assisted-as-needed como herramienta de planificación de sesiones de rehabilitación personalizadas y con un objetivo clínico marcado en las que interviene una ortesis robotizada. Los resultados obtenidos evidencian como, tras la ejecución de ciertos algoritmos sencillos, es posible seleccionar automáticamente una configuración para el algoritmo de control assisted-as-needed que consigue que la ortesis se adapte a los criterios establecidos desde un punto de vista clínico en función del paciente estudiado. Estos resultados invitan a profundizar en el desarrollo de algoritmos más avanzados de selección de parámetros a partir de baterías de simulaciones Estos trabajos han servido para corroborar las hipótesis de investigación planteadas al inicio de la misma, permitiendo, asimismo, la apertura de nuevas líneas de investigación. Summary The World Health Organization (WHO) predicts that by the year 2020, Acquired Brain Injury (ABI) will be among the ten most common ailments. These injuries dramatically change the life of the patients and their families due to their physical, sensory, cognitive, emotional and socio-economic consequences. New techniques of early intervention and the development of intensive ABI care have noticeably improved the survival rate. However, in spite of these advances, brain injuries still have no surgical or pharmacological treatment to re-establish the lost functions. Neurorehabilitation therapies address this problem by restoring, minimizing or compensating the functional alterations in a person disabled because of a nervous system injury. One of the main objectives of Neurorehabilitation is to provide patients with the capacity to perform specific Activities of the Daily Life (ADL) required for an independent life, especially those in which the Upper Limb (UL) is directly involved due to its great importance in manipulating objects within the patients' environment. The incorporation of new technological aids to the neurorehabilitation process tries to reach a new paradigm focused on offering a personalized, monitored and ubiquitous practise with continuous assessment of both the efficacy and the efficiency of the procedures and with the capacity of generating new knowledge. New targets will be to minimize the impact of the sicknesses affecting the functional capabilitiies of the subjects, to decrease the time of the physical handicap and to allow a more efficient resources handling. These targets, of a great socio-economic impact, can only be achieved by means of new technologies and algorithms able to provoke the technological break needed to beat the barriers that are stopping the universal penetration of the technology in the field of rehabilitation. In this way, this PhD Thesis has achieved the following results: 1. ADL Modeling: as a previous step to the incorporation of technological aids to the neurorehabilitation process, it is necessary a first modelling and formalization phase of the knowledge associated to the execution of the activities that are performed as a part of the therapy. In particular, the most complex and therapeutically relevant tasks are the ADLs, whose formalization will produce healthy motion models to be used as a reference for future technological developments. Following a methodology based on UML state-chart diagrams, the ADLs 'serving water from a jar' and 'picking up a bottle' have been modelled 2. Ubiquitous monitoring of the UL movement: it has been designed, developed and validated a motion acquisition system based on inertial technology that improves the limitations of the current devices (high monetary cost and inability of working within uncontrolled environments); the high correlation coefficients and the low error levels obtained throughout several co-registration sessions with the commercial sys- tem BTS SMART-D show the high precision of the system. Besides an exploration of a very low cost stereoscopic vision-based motion capture system has been carried out and the key points where it is necessary to insist from a technological point of view have been detected 3. Inverse Kinematics (IK) problem solving: a solution to the IK problem has been proposed for a manipulator that corresponds to a human UL. This solution has been faced by means of two different alternatives, one based on a Mulilayer Perceptron (MLP) and another based on Artificial Neuro-Fuzzy Inference Systems (ANFIS). The validation of these solutions, carried out using the information regarding the previously generated motion models, indicate that a MLP-based solution, with an architecture consisting in 3 neurons in the input layer, one hidden layer of 3 neurons and an output layer with as many neurons as the number of Degrees of Freedom (DoFs) that the UL model has, is the one that provides the best results both in terms of precission and in terms of processing time, making in idoneous to be integrated within a system with real time restrictions 4. Assisted-as-needed intelligent control: an assisted-as-needed control algorithm with anticipatory actuation capabilities has been designed, developed and validated for a robotic orthosis of which there is an already implemented prototype. Obtained results demonstrate that the control system is able to adapt to the dysfunctional profile of the patient by triggering the assistance right before an incorrect movement is going to take place. This strategy implies an increase in the participation of the patients and in his or her muscle activity, encouraging the neural plasticity processes in charge of the motor learning 5. Planification with a robotic simulator: in this work a robotic simulator is proposed as a planification tool for personalized rehabilitation sessions under a certain clinical criterium. Obtained results indicate that, after the execution of simple parameter selection algorithms, it is possible to automatically choose a specific configuration that makes the assisted-as-needed control algorithm to adapt both to the clinical criteria and to the patient. These results invite researchers to work in the development of more complex parameter selection algorithms departing from simulation batteries Obtained results have been useful to corroborate the hypotheses set out at the beginning of this PhD Thesis. Besides, they have allowed the creation of new research lines in all the studied application fields.

Regularization for sparsity in statistical analysis and machine learning

Pragmatism is the leading motivation of regularization. We can understand regularization as a modification of the maximum-likelihood estimator so that a reasonable answer could be given in an unstable or ill-posed situation. To mention some typical examples, this happens when fitting parametric or non-parametric models with more parameters than data or when estimating large covariance matrices. Regularization is usually used, in addition, to improve the bias-variance tradeoff of an estimation. Then, the definition of regularization is quite general, and, although the introduction of a penalty is probably the most popular type, it is just one out of multiple forms of regularization. In this dissertation, we focus on the applications of regularization for obtaining sparse or parsimonious representations, where only a subset of the inputs is used. A particular form of regularization, L1-regularization, plays a key role for reaching sparsity. Most of the contributions presented here revolve around L1-regularization, although other forms of regularization are explored (also pursuing sparsity in some sense). In addition to present a compact review of L1-regularization and its applications in statistical and machine learning, we devise methodology for regression, supervised classification and structure induction of graphical models. Within the regression paradigm, we focus on kernel smoothing learning, proposing techniques for kernel design that are suitable for high dimensional settings and sparse regression functions. We also present an application of regularized regression techniques for modeling the response of biological neurons. Supervised classification advances deal, on the one hand, with the application of regularization for obtaining a na¨ıve Bayes classifier and, on the other hand, with a novel algorithm for brain-computer interface design that uses group regularization in an efficient manner. Finally, we present a heuristic for inducing structures of Gaussian Bayesian networks using L1-regularization as a filter. El pragmatismo es la principal motivación de la regularización. Podemos entender la regularización como una modificación del estimador de máxima verosimilitud, de tal manera que se pueda dar una respuesta cuando la configuración del problema es inestable. A modo de ejemplo, podemos mencionar el ajuste de modelos paramétricos o no paramétricos cuando hay más parámetros que casos en el conjunto de datos, o la estimación de grandes matrices de covarianzas. Se suele recurrir a la regularización, además, para mejorar el compromiso sesgo-varianza en una estimación. Por tanto, la definición de regularización es muy general y, aunque la introducción de una función de penalización es probablemente el método más popular, éste es sólo uno de entre varias posibilidades. En esta tesis se ha trabajado en aplicaciones de regularización para obtener representaciones dispersas, donde sólo se usa un subconjunto de las entradas. En particular, la regularización L1 juega un papel clave en la búsqueda de dicha dispersión. La mayor parte de las contribuciones presentadas en la tesis giran alrededor de la regularización L1, aunque también se exploran otras formas de regularización (que igualmente persiguen un modelo disperso). Además de presentar una revisión de la regularización L1 y sus aplicaciones en estadística y aprendizaje de máquina, se ha desarrollado metodología para regresión, clasificación supervisada y aprendizaje de estructura en modelos gráficos. Dentro de la regresión, se ha trabajado principalmente en métodos de regresión local, proponiendo técnicas de diseño del kernel que sean adecuadas a configuraciones de alta dimensionalidad y funciones de regresión dispersas. También se presenta una aplicación de las técnicas de regresión regularizada para modelar la respuesta de neuronas reales. Los avances en clasificación supervisada tratan, por una parte, con el uso de regularización para obtener un clasificador naive Bayes y, por otra parte, con el desarrollo de un algoritmo que usa regularización por grupos de una manera eficiente y que se ha aplicado al diseño de interfaces cerebromáquina. Finalmente, se presenta una heurística para inducir la estructura de redes Bayesianas Gaussianas usando regularización L1 a modo de filtro.

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.

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.

A Novel Method for Radio Propagation Simulation Based on Automatic 3D Environment Reconstruction

In this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target regions, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. Our proposition reduces, or even eliminates, infrastructure cost and human efforts during the construction of realistic 3D scenes used in radio propagation modeling. In addition, the results obtained from our propagation model proves to be both accurate and efficient

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.

Problem-based learning supported by semantic techniques

Problem-based learning has been applied over the last three decades to a diverse range of learning environments. In this educational approach, different problems are posed to the learners so that they can develop different solutions while learning about the problem domain. When applied to conceptual modelling, and particularly to Qualitative Reasoning, the solutions to problems are models that represent the behaviour of a dynamic system. The learner?s task then is to bridge the gap between their initial model, as their first attempt to represent the system, and the target models that provide solutions to that problem. We propose the use of semantic technologies and resources to help in bridging that gap by providing links to terminology and formal definitions, and matching techniques to allow learners to benefit from existing models.

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.

Quality in Blended Learning in Higher Education. A proposal for an Evaluation Model.

This paper presents an analysis of different models used to assess the quality of formative actions, considering classroom learning and distance education courses. Taking as starting point one of the analyzed models, the paper sets out the necessity of developing a new model that could measure the quality of a blended formation process, by selecting the applicable indicators and proposing some new. The model is composed of seven different categories, which include a sum of thirty five indicators. They will be used to represent courses quality level in Kiviat?s diagrams. This model is currently being put into practice in a real university environment.

Towards a lightweight mobile semantic-based approach for enhancing interaction with smart objects

This work describes a semantic extension for a user-smart object interaction model based on the ECA paradigm (Event-Condition-Action). In this approach, smart objects publish their sensing (event) and action capabilities in the cloud and mobile devices are prepared to retrieve them and act as mediators to configure personalized behaviours for the objects. In this paper, the information handled by this interaction system has been shaped according several semantic models that, together with the integration of an embedded ontological and rule-based reasoner, are exploited in order to (i) automatically detect incompatible ECA rules configurations and to (ii) support complex ECA rules definitions and execution. This semantic extension may significantly improve the management of smart spaces populated with numerous smart objects from mobile personal devices, as it facilitates the configuration of coherent ECA rules.

A novel method for radio propagation simulation based on automatic 3D environment reconstruction

In this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target region, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. By comparing with other methods, the work presented in this paper makes contributions on reducing human efforts and cost in constructing 3D scene; moreover, the developed propagation model proves its potential in both accuracy and efficiency.

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.

Aerial video geo-registration using terrain models from dense and coherent stereo matching

In the context of aerial imagery, one of the first steps toward a coherent processing of the information contained in multiple images is geo-registration, which consists in assigning geographic 3D coordinates to the pixels of the image. This enables accurate alignment and geo-positioning of multiple images, detection of moving objects and fusion of data acquired from multiple sensors. To solve this problem there are different approaches that require, in addition to a precise characterization of the camera sensor, high resolution referenced images or terrain elevation models, which are usually not publicly available or out of date. Building upon the idea of developing technology that does not need a reference terrain elevation model, we propose a geo-registration technique that applies variational methods to obtain a dense and coherent surface elevation model that is used to replace the reference model. The surface elevation model is built by interpolation of scattered 3D points, which are obtained in a two-step process following a classical stereo pipeline: first, coherent disparity maps between image pairs of a video sequence are estimated and then image point correspondences are back-projected. The proposed variational method enforces continuity of the disparity map not only along epipolar lines (as done by previous geo-registration techniques) but also across them, in the full 2D image domain. In the experiments, aerial images from synthetic video sequences have been used to validate the proposed technique.

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.