l1-penalized projected Bellman residual

International audienceWe consider the task of feature selection for value function approximation in reinforcement learning. A promising approach consists in combining the Least-Squares Temporal Difference (LSTD) algorithm with $\ell_1$-regularization, which has proven to be effective in the supervised learning community. This has been done recently whit the LARS-TD algorithm, which replaces the projection operator of LSTD with an $\ell_1$-penalized projection and solves the corresponding fixed-point problem. However, this approach is not guaranteed to be correct in the general off-policy setting. We take a different route by adding an $\ell_1$-penalty term to the projected Bellman residual, which requires weaker assumptions while offering a comparable performance. However, this comes at the cost of a higher computational complexity if only a part of the regularization path is computed. Nevertheless, our approach ends up to a supervised learning problem, which let envision easy extensions to other penalties

Structured Variable Selection with Sparsity-Inducing Norms

We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual $\ell_1$-norm and the group $\ell_1$-norm by allowing the subsets to overlap. This leads to a specific set of allowed nonzero patterns for the solutions of such problems. We first explore the relationship between the groups defining the norm and the resulting nonzero patterns, providing both forward and backward algorithms to go back and forth from groups to patterns. This allows the design of norms adapted to specific prior knowledge expressed in terms of nonzero patterns. We also present an efficient active set algorithm, and analyze the consistency of variable selection for least-squares linear regression in low and high-dimensional settings

Regularized brain reading with shrinkage and smoothing

Functional neuroimaging measures how the brain responds to complex stimuli. However, sample sizes are modest, noise is substantial, and stimuli are high dimensional. Hence, direct estimates are inherently imprecise and call for regularization. We compare a suite of approaches which regularize via shrinkage: ridge regression, the elastic net (a generalization of ridge regression and the lasso), and a hierarchical Bayesian model based on small area estimation (SAE). We contrast regularization with spatial smoothing and combinations of smoothing and shrinkage. All methods are tested on functional magnetic resonance imaging (fMRI) data from multiple subjects participating in two different experiments related to reading, for both predicting neural response to stimuli and decoding stimuli from responses. Interestingly, when the regularization parameters are chosen by cross-validation independently for every voxel, low/high regularization is chosen in voxels where the classification accuracy is high/low, indicating that the regularization intensity is a good tool for identification of relevant voxels for the cognitive task. Surprisingly, all the regularization methods work about equally well, suggesting that beating basic smoothing and shrinkage will take not only clever methods, but also careful modeling.Comment: Published at http://dx.doi.org/10.1214/15-AOAS837 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Total variation regularization for fMRI-based prediction of behaviour.

International audienceWhile medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of taskrelated or spontaneous neuronal activity, are classically analyzed in a mass-univariate procedure yielding statistical parametric maps. This analysis framework disregards some important principles of brain organization: population coding, distributed and overlapping representations. Multivariate pattern analysis, i.e., the prediction of behavioural variables from brain activation patterns better captures this structure. To cope with the high dimensionality of the data, the learning method has to be regularized. However, the spatial structure of the image is not taken into account in standard regularization methods, so that the extracted features are often hard to interpret. More informative and interpretable results can be obtained with the '1 norm of the image gradient, a.k.a. its Total Variation (TV), as regularization. We apply for the first time this method to fMRI data, and show that TV regularization is well suited to the purpose of brain mapping while being a powerful tool for brain decoding. Moreover, this article presents the first use of TV regularization for classification

Computational Inverse Problems

Inverse problem typically deal with the identification of unknown quantities from indirect measurements and appear in many areas in technology, medicine, biology, finance, and econometrics. The computational solution of such problems is a very active, interdisciplinary field with close connections to optimization, control theory, differential equations, asymptotic analysis, statistics, and probability. The focus of this workshop was on hybrid methods, model reduction, regularization in Banach spaces, and statistical approaches

Interpretable machine learning models for predicting with missing values

Machine learning models are often used in situations where model inputs are missing either during training or at the time of prediction. If missing values are not handled appropriately, they can lead to increased bias or to models that are not applicable in practice without imputing the values of the unobserved variables. However, the imputation of missing values is often inadequate and difficult to interpret for complex imputation functions. In this thesis, we focus on predictions in the presence of incomplete data at test time, using interpretable models that allow humans to understand the predictions. Interpretability is especially necessary when important decisions are at stake, such as in healthcare. First, we investigate, the situation where variables are missing in recurrent patterns and sample sizes are small per pattern. We propose SPSM that allows coefficient sharing between a main model and pattern submodels in order to make efficient use of data and to be independent on imputation. To enable interpretability, the model can be expressed as a short description introduced by sparsity. Then, we explore situations where missingness does not occur in patterns and suggest the sparse linear rule model MINTY that naturally trades off between interpretability and the goodness of fit while being sensitive to missing values at test time. To this end, we learn replacement variables, indicating which features in a rule can be alternatively used when the original feature was not measured, assuming some redundancy in the covariates. Our results have shown that the proposed interpretable models can be used for prediction with missing values, without depending on imputation. We conclude that more work can be done in evaluating interpretable machine learning models in the context of missing values at test time

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