Study of regularisation methods in machine learning

在过去的十年中，功能强大的计算机的出现为机器学习技术在复杂的应用领域中的使用打开了大门，例如在计算机视觉、语音识别、计算语言学、营销科学和生物信息学中出现的那些领域，仅举几例。机器学习中已被证明在上述领域中有价值的中心方法包括通过最小化正则化误差泛函来从可用数据计算函数，该正则化误差泛函平衡不同的错误/惩罚标准。例如，正则化误差泛函可以涉及测量数据上的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讨正规化方法在机器学习中的理论和实践影响，并就这一主题编写一本书的初稿。米切利教授和庞蒂尔博士对机器学习有着浓厚的兴趣，拟议中的访问将是他们在广泛的时间段内合作的第一次机会。米切利在计算数学领域的世界领导者中名列前茅。他在这个领域做出了根本性的贡献，特别是在关于函数的逼近、表示和估计的问题上。他的工作不仅对主流数学产生了影响，还对附近的领域产生了影响，特别是在统计学和计算机科学领域。他是最近ISI列出的世界上被引用最多的200名数学家之一。

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.