PAC-Bayes learning and Kernel methods

机器学习关注的是智能计算机系统的发展，这些系统能够从收集的数据中学习和归纳。在许多应用程序域中都需要此功能。例如，在计算机视觉中，我们感兴趣的是学习从一组带注释的图像中识别场景(以及场景中的一些对象)。在生物信息学中，我们希望能够通过从包含几个结合在一起的分子-蛋白质对的实例的数据库中学习来预测哪个分子可以与给定的蛋白质结合。在机器翻译中，我们希望能够通过从一组由人类翻译的文本样本中学习这项任务，将文本从一种语言翻译成另一种语言。许多像这样的重要应用程序强烈依赖于构建准确预测器的底层学习算法的性能。这项研究计划的长期目标是提出能够满足这种大规模应用的要求的学习算法，从而提高我们的生活质量。为了朝着这个目标前进，我们计划扩大我们之前在学习算法方面的工作，这些算法优化了对预测者准确性的严格保证，称为风险界限。更具体地说，我们将专注于核方法，通过扩展我们之前关于PAC-贝叶斯样本压缩的工作，我们将开发用于学习核的PAC-贝叶斯界最小化算法。我们还计划提出新的学习算法来构造结构化输出预测器和其他预测器，这些预测器比支持向量机更通用，可能更强大。

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.