Rational optimization for nonlinear reconstruction with approximate ℓ0 penalization

International audienceRecovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the nonlinearity of the model can be accounted for by a rational function. In addition, we suppose that the signal to be sought is sparse and a rational approximation of the ℓ0 pseudo-norm thus constitutes a suitable penalization. The resulting composite cost function belongs to the broad class of semi-algebraic functions. To find a globally optimal solution to such an optimization problem, it can be transformed into a generalized moment problem, for which a hierarchy of semidefinite programming relaxations can be built. Global optimality comes at the expense of an increased dimension and, to overcome computational limitations concerning the number of involved variables, the structure of the problem has to be carefully addressed. A situation of practical interest is when the nonlinear model consists of a convolutive transform followed by a componentwise nonlinear rational saturation. We then propose to use a sparse relaxation able to deal with up to several hundreds of optimized variables. In contrast with the naive approach consisting of linearizing the model, our experiments show that the proposed approach offers good performanc

A Fixed Point Framework for Recovering Signals from Nonlinear Transformations

We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the nonlinearities. We show that, in many common applications, the transformation model can be associated with fixed point equations involving firmly nonexpansive operators. In turn, the recovery problem is reduced to a tractable common fixed point formulation, which is solved efficiently by a provably convergent, block-iterative algorithm. Applications to signal and image recovery are demonstrated. Inconsistent problems are also addressed.Comment: 5 page

An Adaptive Phase-Field Method for Structural Topology Optimization

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the objective functional. The adaptive algorithm is provably convergent in the sense that the sequence of numerical approximations generated by the adaptive algorithm contains a subsequence convergent to a solution of the continuous first-order optimality system. We provide several numerical simulations to show the distinct features of the algorithm.Comment: 30 pages, 10 figure

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Big Data Analytics and Information Science for Business and Biomedical Applications

The analysis of Big Data in biomedical as well as business and financial research has drawn much attention from researchers worldwide. This book provides a platform for the deep discussion of state-of-the-art statistical methods developed for the analysis of Big Data in these areas. Both applied and theoretical contributions are showcased

Robust Algorithms for Linear and Nonlinear Regression via Sparse Modeling Methods: Theory, Algorithms and Applications to Image Denoising

Η εύρωστη παλινδρόμηση κατέχει έναν πολύ σημαντικό ρόλο στην Επεξεργασία Σήματος, τη Στατιστική και τη Μηχανική Μάθηση. Συνήθεις εκτιμητές, όπως τα «Ελάχιστα Τετράγωνα», αποτυγχάνουν να εκτιμήσουν σωστά παραμέτρους, όταν στα δεδομένα υπεισέρχονται ακραίες παρατηρήσεις, γνωστές ως “outliers”. Το πρόβλημα αυτό είναι γνωστό εδώ και δεκαετίες, μέσα στις οποίες διάφορες μέθοδοι έχουν προταθεί. Παρόλα αυτά, το ενδιαφέρον της επιστημονικής κοινότητας για αυτό αναζωπυρώθηκε όταν επανεξετάστηκε υπό το πρίσμα της αραιής μοντελοποίησης και των αντίστοιχων τεχνικών, η οποία κυριαρχεί στον τομέα της μηχανικής μάθησης εδώ και δύο δεκαετίες. Αυτή είναι και η κατεύθυνση η οποία ακολουθήθηκε στην παρούσα διατριβή. Το αποτέλεσμα αυτής της εργασίας ήταν η ανάπτυξη μιας νέας προσέγγισης, βασισμένης σε άπληστες τεχνικές αραιής μοντελοποίησης. Το μοντέλο που υιοθετείται βασίζεται στην ανάλυση του θορύβου σε δύο συνιστώσες: α) μια για το συμβατικό (αναμενόμενο) θόρυβο και β) μια για τις ακραίες παρατηρήσεις (outliers), οι οποίες θεωρήθηκε ότι είναι λίγες (αραιές) σε σχέση με τον αριθμό των δεδομένων. Με βάση αυτή τη μοντελοποίηση και τον γνωστό άπληστο αλγόριθμο “Orthogonal Matching Pursuit” (OMP), δύο νέοι αλγόριθμοι αναπτύχθηκαν, ένας για το γραμμικό και ένας για το μη γραμμικό πρόβλημα της εύρωστης παλινδρόμησης. Ο προτεινόμενος αλγόριθμος για τη γραμμική παλινδρόμηση ονομάζεται “Greedy Algorithm for Robust Demoising” (GARD) και εναλλάσσει τα βήματά του μεταξύ της μεθόδου Ελαχίστων Τετραγώνων (LS) και της αναγνώρισης των ακραίων παρατηρήσεων, τεχνικής που βασίζεται στον OMP. Στη συνέχεια, ακολουθεί η σύγκριση της νέας μεθόδου με ανταγωνιστικές της. Συγκεκριμένα, από τα αποτελέσματα παρατηρείται ότι ο GARD: α) δείχνει ανοχή σε ακραίες τιμές (εύρωστος), β) καταφέρνει να προσεγγίσει τη λύση με πολύ μικρό λάθος και γ) απαιτεί μικρό υπολογιστικό κόστος. Επιπλέον, προκύπτουν σημαντικά θεωρητικά ευρήματα, τα οποία οφείλονται στην απλότητα της μεθόδου. Αρχικά, αποδεικνύεται ότι η μέθοδος συγκλίνει σε πεπερασμένο αριθμό βημάτων. Στη συνέχεια, η μελέτη επικεντρώνεται στην αναγνώριση των ακραίων παρατηρήσεων. Το γεγονός ότι η περίπτωση απουσίας συμβατικού θορύβου μελετήθηκε ξεχωριστά, οφείλεται κυρίως στα εξής: α) στην απλοποίηση απαιτητικών πράξεων και β) στην ανάδειξη σημαντικών γεωμετρικών ιδιοτήτων. Συγκεκριμένα, προέκυψε κατάλληλο φράγμα για τη σταθερά της συνθήκης «Περιορισμένης Ισομετρίας» (“Restricted Isometry Property” - (RIP)), το οποίο εξασφαλίζει ότι η ανάκτηση του σήματος μέσω του GARD είναι ακριβής (μηδενικό σφάλμα). Τέλος, για την περίπτωση όπου ακραίες τιμές και συμβατικός θόρυβος συνυπάρχουν και με την παραδοχή ότι το διάνυσμα του συμβατικού θορύβου είναι φραγμένο, προέκυψε μια αντίστοιχη συνθήκη η οποία εξασφαλίζει την ανάκτηση του φορέα του αραιού διανύσματος θορύβου (outliers). Δεδομένου ότι μια τέτοια συνθήκη ικανοποιείται, αποδείχθηκε ότι το σφάλμα προσέγγισης είναι φραγμένο και άρα ο εκτιμητής GARD ευσταθής. Για το πρόβλημα της εύρωστης μη γραμμικής παλινδρόμησης, θεωρείται, επιπλέον, ότι η άγνωστη μη γραμμική συνάρτηση ανήκει σε ένα χώρο Hilbert με αναπαραγωγικούς πυρήνες (RKHS). Λόγω της ύπαρξης ακραίων παρατηρήσεων, τεχνικές όπως το Kernel Ridge Regression (KRR) ή το Support Vector Regression (SVR) αποδεικνύονται ανεπαρκείς. Βασισμένοι στην προαναφερθείσα ανάλυση των συνιστωσών του θορύβου και χρησιμοποιώντας την τεχνική της αραιής μοντελοποίησης, πραγματοποιείται η εκτίμηση των ακραίων παρατηρήσεων σύμφωνα με τα βήματα μιας άπληστης επαναληπτικής διαδικασίας. Ο προτεινόμενος αλγόριθμος ονομάζεται “Kernel Greedy Algorithm for Robust Denoising” (KGARD), και εναλλάσσει τα βήματά μεταξύ ενός εκτιμητή KRR και της αναγνώρισης ακραίων παρατηρήσεων, με βάση τον OMP. Αναλύεται θεωρητικά η ικανότητα του αλγορίθμου να αναγνωρίσει τις πιθανές ακραίες παρατηρήσεις. Επιπλέον, ο αλγόριθμος KGARD συγκρίνεται με άλλες μεθόδους αιχμής μέσα από εκτεταμένο αριθμό πειραμάτων, όπου και παρατηρείται η σαφώς καλύτερη απόδοσή του. Τέλος, η προτεινόμενη μέθοδος για την εύρωστη παλινδρόμηση εφαρμόζεται στην αποθορύβωση εικόνας, όπου αναδεικνύονται τα σαφή πλεονεκτήματα της μεθόδου. Τα πειράματα επιβεβαιώνουν ότι ο αλγόριθμος KGARD βελτιώνει σημαντικά την διαδικασία της αποθορύβωσης, στην περίπτωση όπου στον θόρυβο υπεισέρχονται ακραίες παρατηρήσεις.The task of robust regression is of particular importance in signal processing, statistics and machine learning. Ordinary estimators, such as the Least Squares (LS) one, fail to achieve sufficiently good performance in the presence of outliers. Although the problem has been addressed many decades ago and several methods have been established, it has recently attracted more attention in the context of sparse modeling and sparse optimization techniques. The latter is the line that has been followed in the current dissertation. The reported research, led to the development of a novel approach in the context of greedy algorithms. The model adopts the decomposition of the noise into two parts: a) the inlier noise and b) the outliers, which are explicitly modeled by employing sparse modeling arguments. Based on this rationale and inspired by the popular Orthogonal Matching Pursuit (OMP), two novel efficient greedy algorithms are established, one for the linear and another one for the nonlinear robust regression task. The proposed algorithm for the linear task, i.e., Greedy Algorithm for Robust Denoising (GARD), alternates between a Least Squares (LS) optimization criterion and an OMP selection step, that identifies the outliers. The method is compared against state-of-the-art methods through extensive simulations and the results demonstrate that: a) it exhibits tolerance in the presence of outliers, i.e., robustness, b) it attains a very low approximation error and c) it has relatively low computational requirements. Moreover, due to the simplicity of the method, a number of related theoretical properties are derived. Initially, the convergence of the method in a finite number of iteration steps is established. Next, the focus of the theoretical analysis is turned on the identification of the outliers. The case where only outliers are present has been studied separately; this is mainly due to the following reasons: a) the simplification of technically demanding algebraic manipulations and b) the “articulation” of the method’s interesting geometrical properties. In particular, a bound based on the Restricted Isometry Property (RIP) constant guarantees that the recovery of the signal via GARD is exact (zero error). Finally, for the case where outliers as well as inlier noise coexist, and by assuming that the inlier noise vector is bounded, a similar condition that guarantees the recovery of the support for the sparse outlier vector is derived. If such a condition is satisfied, then it is shown that the approximation error is bounded, and thus the denoising estimator is stable. For the robust nonlinear regression task, it is assumed that the unknown nonlinear function belongs to a Reproducing Kernel Hilbert Space (RKHS). Due to the existence of outliers, common techniques such as the Kernel Ridge Regression (KRR), or the Support Vector Regression (SVR) turn out to be inadequate. By employing the aforementioned noise decomposition, sparse modeling arguments are employed so that the outliers are estimated according to the greedy approach. The proposed robust scheme, i.e., Kernel Greedy Algorithm for Robust Denoising (KGARD), alternates between a KRR task and an OMP-like selection step. Theoretical results regarding the identification of the outliers are provided. Moreover, KGARD is compared against other cutting edge methods via extensive simulations, where its enhanced performance is demonstrated. Finally, the proposed robust estimation framework is applied to the task of image denoising, where the advantages of the proposed method are unveiled. The experiments verify that KGARD improves the denoising process significantly, when outliers are present

Mathematical control theory and Finance

Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn the attention of the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic control. We strongly believe in the possibility of a fruitful collaboration between specialists of deterministic and stochastic control theory and specialists in finance, both from academic and business backgrounds. It is this kind of collaboration that the organizers of the Workshop on Mathematical Control Theory and Finance wished to foster. This volume collects a set of original papers based on plenary lectures and selected contributed talks presented at the Workshop. They cover a wide range of current research topics on the mathematics of control systems and applications to finance. They should appeal to all those who are interested in research at the junction of these three important fields as well as those who seek special topics within this scope.info:eu-repo/semantics/publishedVersio

An adaptive, fault-tolerant system for road network traffic prediction using machine learning

This thesis has addressed the design and development of an integrated system for real-time traffic forecasting based on machine learning methods. Although traffic prediction has been the driving motivation for the thesis development, a great part of the proposed ideas and scientific contributions in this thesis are generic enough to be applied in any other problem where, ideally, their definition is that of the flow of information in a graph-like structure. Such application is of special interest in environments susceptible to changes in the underlying data generation process. Moreover, the modular architecture of the proposed solution facilitates the adoption of small changes to the components that allow it to be adapted to a broader range of problems. On the other hand, certain specific parts of this thesis are strongly tied to the traffic flow theory. The focus in this thesis is on a macroscopic perspective of the traffic flow where the individual road traffic flows are correlated to the underlying traffic demand. These short-term forecasts include the road network characterization in terms of the corresponding traffic measurements –traffic flow, density and/or speed–, the traffic state –whether a road is congested or not, and its severity–, and anomalous road conditions –incidents or other non-recurrent events–. The main traffic data used in this thesis is data coming from detectors installed along the road networks. Nevertheless, other kinds of traffic data sources could be equally suitable with the appropriate preprocessing. This thesis has been developed in the context of Aimsun Live –a simulation-based traffic solution for real-time traffic prediction developed by Aimsun–. The methods proposed here is planned to be linked to it in a mutually beneficial relationship where they cooperate and assist each other. An example is when an incident or non-recurrent event is detected with the proposed methods in this thesis, then the simulation-based forecasting module can simulate different strategies to measure their impact. Part of this thesis has been also developed in the context of the EU research project "SETA" (H2020-ICT-2015). The main motivation that has guided the development of this thesis is enhancing those weak points and limitations previously identified in Aimsun Live, and whose research found in literature has not been especially extensive. These include: • Autonomy, both in the preparation and real-time stages. • Adaptation, to gradual or abrupt changes in traffic demand or supply. • Informativeness, about anomalous road conditions. • Forecasting accuracy improved with respect to previous methodology at Aimsun and a typical forecasting baseline. • Robustness, to deal with faulty or missing data in real-time. • Interpretability, adopting modelling choices towards a more transparent reasoning and understanding of the underlying data-driven decisions. • Scalable, using a modular architecture with emphasis on a parallelizable exploitation of large amounts of data. The result of this thesis is an integrated system –Adarules– for real-time forecasting which is able to make the best of the available historical data, while at the same time it also leverages the theoretical unbounded size of data in a continuously streaming scenario. This is achieved through the online learning and change detection features along with the automatic finding and maintenance of patterns in the network graph. In addition to the Adarules system, another result is a probabilistic model that characterizes a set of interpretable latent variables related to the traffic state based on the traffic data provided by the sensors along with optional prior knowledge provided by the traffic expert following a Bayesian approach. On top of this traffic state model, it is built the probabilistic spatiotemporal model that learns the dynamics of the transition of traffic states in the network, and whose objectives include the automatic incident detection.Esta tesis ha abordado el diseño y desarrollo de un sistema integrado para la predicción de tráfico en tiempo real basándose en métodos de aprendizaje automático. Aunque la predicción de tráfico ha sido la motivación que ha guiado el desarrollo de la tesis, gran parte de las ideas y aportaciones científicas propuestas en esta tesis son lo suficientemente genéricas como para ser aplicadas en cualquier otro problema en el que, idealmente, su definición sea la del flujo de información en una estructura de grafo. Esta aplicación es de especial interés en entornos susceptibles a cambios en el proceso de generación de datos. Además, la arquitectura modular facilita la adaptación a una gama más amplia de problemas. Por otra parte, ciertas partes específicas de esta tesis están fuertemente ligadas a la teoría del flujo de tráfico. El enfoque de esta tesis se centra en una perspectiva macroscópica del flujo de tráfico en la que los flujos individuales están ligados a la demanda de tráfico subyacente. Las predicciones a corto plazo incluyen la caracterización de las carreteras en base a las medidas de tráfico -flujo, densidad y/o velocidad-, el estado del tráfico -si la carretera está congestionada o no, y su severidad-, y la detección de condiciones anómalas -incidentes u otros eventos no recurrentes-. Los datos utilizados en esta tesis proceden de detectores instalados a lo largo de las redes de carreteras. No obstante, otros tipos de fuentes de datos podrían ser igualmente empleados con el preprocesamiento apropiado. Esta tesis ha sido desarrollada en el contexto de Aimsun Live -software desarrollado por Aimsun, basado en simulación para la predicción en tiempo real de tráfico-. Los métodos aquí propuestos cooperarán con este. Un ejemplo es cuando se detecta un incidente o un evento no recurrente, entonces pueden simularse diferentes estrategias para medir su impacto. Parte de esta tesis también ha sido desarrollada en el marco del proyecto de la UE "SETA" (H2020-ICT-2015). La principal motivación que ha guiado el desarrollo de esta tesis es mejorar aquellas limitaciones previamente identificadas en Aimsun Live, y cuya investigación encontrada en la literatura no ha sido muy extensa. Estos incluyen: -Autonomía, tanto en la etapa de preparación como en la de tiempo real. -Adaptación, a los cambios graduales o abruptos de la demanda u oferta de tráfico. -Sistema informativo, sobre las condiciones anómalas de la carretera. -Mejora en la precisión de las predicciones con respecto a la metodología anterior de Aimsun y a un método típico usado como referencia. -Robustez, para hacer frente a datos defectuosos o faltantes en tiempo real. -Interpretabilidad, adoptando criterios de modelización hacia un razonamiento más transparente para un humano. -Escalable, utilizando una arquitectura modular con énfasis en una explotación paralela de grandes cantidades de datos. El resultado de esta tesis es un sistema integrado –Adarules- para la predicción en tiempo real que sabe maximizar el provecho de los datos históricos disponibles, mientras que al mismo tiempo también sabe aprovechar el tamaño teórico ilimitado de los datos en un escenario de streaming. Esto se logra a través del aprendizaje en línea y la capacidad de detección de cambios junto con la búsqueda automática y el mantenimiento de los patrones en la estructura de grafo de la red. Además del sistema Adarules, otro resultado de la tesis es un modelo probabilístico que caracteriza un conjunto de variables latentes interpretables relacionadas con el estado del tráfico basado en los datos de sensores junto con el conocimiento previo –opcional- proporcionado por el experto en tráfico utilizando un planteamiento Bayesiano. Sobre este modelo de estados de tráfico se construye el modelo espacio-temporal probabilístico que aprende la dinámica de la transición de estado

An adaptive, fault-tolerant system for road network traffic prediction using machine learning

This thesis has addressed the design and development of an integrated system for real-time traffic forecasting based on machine learning methods. Although traffic prediction has been the driving motivation for the thesis development, a great part of the proposed ideas and scientific contributions in this thesis are generic enough to be applied in any other problem where, ideally, their definition is that of the flow of information in a graph-like structure. Such application is of special interest in environments susceptible to changes in the underlying data generation process. Moreover, the modular architecture of the proposed solution facilitates the adoption of small changes to the components that allow it to be adapted to a broader range of problems. On the other hand, certain specific parts of this thesis are strongly tied to the traffic flow theory. The focus in this thesis is on a macroscopic perspective of the traffic flow where the individual road traffic flows are correlated to the underlying traffic demand. These short-term forecasts include the road network characterization in terms of the corresponding traffic measurements –traffic flow, density and/or speed–, the traffic state –whether a road is congested or not, and its severity–, and anomalous road conditions –incidents or other non-recurrent events–. The main traffic data used in this thesis is data coming from detectors installed along the road networks. Nevertheless, other kinds of traffic data sources could be equally suitable with the appropriate preprocessing. This thesis has been developed in the context of Aimsun Live –a simulation-based traffic solution for real-time traffic prediction developed by Aimsun–. The methods proposed here is planned to be linked to it in a mutually beneficial relationship where they cooperate and assist each other. An example is when an incident or non-recurrent event is detected with the proposed methods in this thesis, then the simulation-based forecasting module can simulate different strategies to measure their impact. Part of this thesis has been also developed in the context of the EU research project "SETA" (H2020-ICT-2015). The main motivation that has guided the development of this thesis is enhancing those weak points and limitations previously identified in Aimsun Live, and whose research found in literature has not been especially extensive. These include: • Autonomy, both in the preparation and real-time stages. • Adaptation, to gradual or abrupt changes in traffic demand or supply. • Informativeness, about anomalous road conditions. • Forecasting accuracy improved with respect to previous methodology at Aimsun and a typical forecasting baseline. • Robustness, to deal with faulty or missing data in real-time. • Interpretability, adopting modelling choices towards a more transparent reasoning and understanding of the underlying data-driven decisions. • Scalable, using a modular architecture with emphasis on a parallelizable exploitation of large amounts of data. The result of this thesis is an integrated system –Adarules– for real-time forecasting which is able to make the best of the available historical data, while at the same time it also leverages the theoretical unbounded size of data in a continuously streaming scenario. This is achieved through the online learning and change detection features along with the automatic finding and maintenance of patterns in the network graph. In addition to the Adarules system, another result is a probabilistic model that characterizes a set of interpretable latent variables related to the traffic state based on the traffic data provided by the sensors along with optional prior knowledge provided by the traffic expert following a Bayesian approach. On top of this traffic state model, it is built the probabilistic spatiotemporal model that learns the dynamics of the transition of traffic states in the network, and whose objectives include the automatic incident detection.Esta tesis ha abordado el diseño y desarrollo de un sistema integrado para la predicción de tráfico en tiempo real basándose en métodos de aprendizaje automático. Aunque la predicción de tráfico ha sido la motivación que ha guiado el desarrollo de la tesis, gran parte de las ideas y aportaciones científicas propuestas en esta tesis son lo suficientemente genéricas como para ser aplicadas en cualquier otro problema en el que, idealmente, su definición sea la del flujo de información en una estructura de grafo. Esta aplicación es de especial interés en entornos susceptibles a cambios en el proceso de generación de datos. Además, la arquitectura modular facilita la adaptación a una gama más amplia de problemas. Por otra parte, ciertas partes específicas de esta tesis están fuertemente ligadas a la teoría del flujo de tráfico. El enfoque de esta tesis se centra en una perspectiva macroscópica del flujo de tráfico en la que los flujos individuales están ligados a la demanda de tráfico subyacente. Las predicciones a corto plazo incluyen la caracterización de las carreteras en base a las medidas de tráfico -flujo, densidad y/o velocidad-, el estado del tráfico -si la carretera está congestionada o no, y su severidad-, y la detección de condiciones anómalas -incidentes u otros eventos no recurrentes-. Los datos utilizados en esta tesis proceden de detectores instalados a lo largo de las redes de carreteras. No obstante, otros tipos de fuentes de datos podrían ser igualmente empleados con el preprocesamiento apropiado. Esta tesis ha sido desarrollada en el contexto de Aimsun Live -software desarrollado por Aimsun, basado en simulación para la predicción en tiempo real de tráfico-. Los métodos aquí propuestos cooperarán con este. Un ejemplo es cuando se detecta un incidente o un evento no recurrente, entonces pueden simularse diferentes estrategias para medir su impacto. Parte de esta tesis también ha sido desarrollada en el marco del proyecto de la UE "SETA" (H2020-ICT-2015). La principal motivación que ha guiado el desarrollo de esta tesis es mejorar aquellas limitaciones previamente identificadas en Aimsun Live, y cuya investigación encontrada en la literatura no ha sido muy extensa. Estos incluyen: -Autonomía, tanto en la etapa de preparación como en la de tiempo real. -Adaptación, a los cambios graduales o abruptos de la demanda u oferta de tráfico. -Sistema informativo, sobre las condiciones anómalas de la carretera. -Mejora en la precisión de las predicciones con respecto a la metodología anterior de Aimsun y a un método típico usado como referencia. -Robustez, para hacer frente a datos defectuosos o faltantes en tiempo real. -Interpretabilidad, adoptando criterios de modelización hacia un razonamiento más transparente para un humano. -Escalable, utilizando una arquitectura modular con énfasis en una explotación paralela de grandes cantidades de datos. El resultado de esta tesis es un sistema integrado –Adarules- para la predicción en tiempo real que sabe maximizar el provecho de los datos históricos disponibles, mientras que al mismo tiempo también sabe aprovechar el tamaño teórico ilimitado de los datos en un escenario de streaming. Esto se logra a través del aprendizaje en línea y la capacidad de detección de cambios junto con la búsqueda automática y el mantenimiento de los patrones en la estructura de grafo de la red. Además del sistema Adarules, otro resultado de la tesis es un modelo probabilístico que caracteriza un conjunto de variables latentes interpretables relacionadas con el estado del tráfico basado en los datos de sensores junto con el conocimiento previo –opcional- proporcionado por el experto en tráfico utilizando un planteamiento Bayesiano. Sobre este modelo de estados de tráfico se construye el modelo espacio-temporal probabilístico que aprende la dinámica de la transición de estadosPostprint (published version