PAC-Bayes learning and Kernel methods

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Machine learning is concerned with the development of intelligent computer systems that are able to learn and generalize from collected data. This ability is required in many application domains. In computer vision for example, we are interested in learning to recognize a scene (and some objects within the scene) from a collection of annotated images. In bioinformatics, we would like to be able to predict which molecule can bind to a given protein by learning from a database containing several examples of molecule-protein pairs that bind together. In machine translation, we would like to be able to translate text from one language to another by learning this task from a set of text samples that have been translated by humans. Many important applications like these strongly rely on the performance of an underlying learning algorithm for constructing accurate predictors. The long-term objective of this research program is to propose learning algorithms that will meet the requirements of such large-scale applications that can improve our quality of life. To progress towards this goal, we plan to expand our previous work on learning algorithms that optimize a rigorous guarantee on the accuracy of predictors, called a risk bound. More specifically, we will focus on kernel methods and, by extending our previous work on PAC-Bayes sample-compression, we will develop PAC-Bayes bound-minimizing algorithms for learning the kernel. We also plan to propose novel learning algorithms for constructing structured output predictors and other predictors that are more general and potentially more powerful than the support vector machine.