Kernel methods in machine learning

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning from the mistakes of others: matching errors in cross dataset learning

Can we learn about object classes in images by looking at a collection of relevant 3D models? Or if we want to learn about human (inter-)actions in images, can we benefit from videos or abstract illustrations that show these actions? A common aspect of these settings is the availability of additional or privileged data that can be exploited at training time and that will not be available and not of interest at test time. We seek to generalize the learning with privileged information (LUPI) framework, which requires additional information to be defined per image, to the setting where additional information is a data collection about the task of interest. Our framework minimizes the distribution mismatch between errors made in images and in privileged data. The proposed method is tested on four publicly available datasets: Image+ClipArt, Image+3Dobject, and Image+Video. Experimental results reveal that our new LUPI paradigm naturally addresses the cross-dataset learning

Machine Learning (ML) module

Lectures notes of the machine learning content of the course TOML (Topics on Optimization and Machine Learning) at Master in Innovation and Research in Informatics (MIRI) at FIB, UPC.2023/202

Regularized approximate policy iteration using kernel for on-line reinforcement learning

By using Reinforcement Learning (RL), an autonomous agent interacting with the environment can learn how to take adequate actions for every situation in order to optimally achieve its own goal. RL provides a general methodology able to solve uncertain and complex decision problems which may be present in many real-world applications. RL problems are usually modeled as a Markov Decision Processes (MDPs) deeply studied in the literature. The main peculiarity of a RL algorithm is that the RL agent is assumed to learn the optimal policies from its experiences without knowing the parameters of the MDP. The key element in solving the MDP is learning a value function which gives the expectation of total reward an agent might expect at its current state taking a given action. This value function allows to obtain the optimal policy. In this thesis we study the capacity of SVR using kernel methods to adapt and solve complex RL problems in large or continuous state space. SVR can be studied using a geometrical interpretation in terms of optimal margin or can be seen as a regularization problem given in a Reproducing Kernel Hilbert Space (RKHS) SVR have good properties over the generalization ability and as they are based a on convex optimization problem, they do not suffer from sub-optimality. SVR are non-parametric showing the ability to automatically adapt to the complexity of the problem. Accordingly, applying SVR to approximate value functions sounds to be a good approach. SVR can be solved both in batch mode when the whole set of training sample are at disposal of the learning agents or incrementally which enables the addition or removal of training samples very effectively. Incremental SVR finds the appropriate KKT conditions for new or updated data by modifying their influences into the regression function maintaining consistence in the KKT conditions for the rest of data used for learning. In RL problems an incremental SVR should be able to approximate the action value function leading to the optimal policy. Accordingly, computation load should be lower, learning speed faster and generalization more effective than other existing method The overall contribution coming from of our work is to develop, formalize, implement and study a new RL technique for generalization in discrete and continuous state spaces with finite actions. Our method uses the Approximate Policy Iteration (API) framework with the BRM criterion which allows to represent the action value function using SVR. This approach for RL is the first one we know using SVR compatible to the agent interaction- with-the-environment framework of RL which shows his power by solving a large number of benchmark problems, including very difficult ones, like the bicycle driving and riding control problem. In addition, unlike most RL approaches to generalization, we develop a proof finding theoretical bounds for the convergence of the method to the optimal solution under given conditions.Mediante el uso de aprendizaje por refuerzo (RL), un agente autónomo interactuando con el medio ambiente puede aprender a tomar adecuada acciones para cada situación con el fin de lograr de manera óptima su propia meta. RL proporciona una metodología general capaz de resolver problemas de decisión complejos que pueden estar presentes en muchas aplicaciones del mundo real. Problemas RL usualmente se modelan como una Procesos de Decisión de Markov (MDP) estudiados profundamente en la literatura. La principal peculiaridad de un algoritmo de RL es que el agente es asumido para aprender las políticas óptimas de sus experiencias sin saber los parámetros de la MDP. El elemento clave en resolver el MDP está en el aprender una función de valor que da la expectativa de recompensa total que un agente puede esperar en su estado actual para tomar una acción determinada. Esta función de valor permite obtener la política óptima. En esta tesis se estudia la capacidad del SVR utilizando núcleo métodos para adaptarse y resolver problemas RL complejas en el espacio estado grande o continua. RVS puede ser estudiado mediante un interpretación geométrica en términos de margen óptimo o puede ser visto como un problema de regularización dado en un Reproducing Kernel Hilbert Space (RKHS). SVR tiene buenas propiedades sobre la capacidad de generalización y ya que se basan en una optimización convexa problema, ellos no sufren de sub-optimalidad. SVR son no paramétrico que muestra la capacidad de adaptarse automáticamente a la complejidad del problema. En consecuencia, la aplicación de RVS para aproximar funciones de valor suena para ser un buen enfoque. SVR puede resolver tanto en modo batch cuando todo el conjunto de muestra de entrenamiento están a disposición de los agentes de aprendizaje o incrementalmente que permite la adición o eliminación de muestras de entrenamiento muy eficaz. Incremental SVR encuentra las condiciones adecuadas para KKT nuevas o actualizadas de datos modificando sus influencias en la función de regresión mantener consistencia en las condiciones KKT para el resto de los datos utilizados para el aprendizaje. En los problemas de RL una RVS elemental será capaz de aproximar la función de valor de acción que conduce a la política óptima. En consecuencia, la carga de cálculo debería ser menor, la velocidad de aprendizaje más rápido y generalización más efectivo que el otro método existente La contribución general que viene de nuestro trabajo es desarrollar, formalizar, ejecutar y estudiar una nueva técnica de RL para la generalización en espacio de estados discretos y continuos con acciones finitas. Nuestro método utiliza el marco de la Approximate Policy Iteration (API) con el criterio de BRM que permite representar la función de valor de acción utilizando SVR. Este enfoque de RL es el primero que conocemos usando SVR compatible con el marco de RL con agentes interaccionado con el ambiente que muestra su poder mediante la resolución de un gran número de problemas de referencia, incluyendo los muy difíciles, como la conducción de bicicletas y problema de control de conducción. Además, a diferencia de la mayoría RL se acerca a la generalización, desarrollamos un hallazgo prueba límites teóricos para la convergencia del método a la solución óptima en condiciones dadas.Postprint (published version