Study of regularisation methods in machine learning

在过去的十年中，强大的计算机的可用性为机器学习技术在复杂应用领域的应用打开了大门，例如计算机视觉、语音识别、计算语言学、市场营销科学和生物信息学等。机器学习的一个核心方法在上述领域被证明是有价值的，它包括通过最小化正则化误差函数来计算可用数据的函数，该函数平衡了不同的错误/惩罚标准。例如，正则化误差函数可能包括测量数据经验误差的数据项和测量函数复杂性的惩罚项的组合。在2006年1月至6月期间，这次访问的目标是继续探索机器学习中正则化方法的理论和实践含义，并就这一主题编写一本书的初稿。Micchelli教授和Pontil博士对机器学习有着浓厚的兴趣，此次访问将是他们第一次有机会在很长一段时间内一起工作。米歇尔在世界计算数学领域名列前茅。他在该领域做出了基础性的贡献，特别是在关于函数的近似、表示和估计的问题上。他的工作不仅在主流数学领域，而且在附近的领域，特别是在统计学和计算机科学领域都有影响。他是最近ISI全球200位被引用最多的数学家之一。

Over the past decade the availability of powerful computers has opened the doors to the use of machine learning techniques in complex application domains such as those arising in computer vision, speech recognition, computational linguistics, marketing science, and bioinformatics, to mention but a few.A central approach in machine learning which has proved valuable in the above domains consists in computing a function from available data by minimising a regularisation error functional which balances different error/penalty criteria. For example, the regularisation error functional may involves the combination of a data term, measuring the empirical error on the data and a penalty term measuring the function complexity. The goal of this visit, during the period of January--June 2006, is to continue to explore both the theoretical and practical implications of the regularisation approach in machine learning as well as produce a first draft of a book on this topic. Prof. Micchelli shares a strong interest with Dr. Pontil in machine learning and the proposed visit will be the first opportunity for them to work together for an extensive period of time.Prof. Micchelli ranks high among the world leaders in computational mathematics. He has made fundamental contributions to that field, especially to problems concerning approximation, representation and estimation of functions. His work has been influential not only in mainstream mathematics but also in nearby fields, particularly in statistics and computer science. He is in the recent ISI list of 200 mathematicians world-wide who are most highly cited.