基于凸正则化项的多核学习算法的理论研究

Kernel methods such as Support Vector Machine have been widely used in machine learning and statistics. The performance of a kernel machine largely depends on the choice of kernel function. To handle this problem, many methods for learning kernel have been proposed in recent years. However, until now there has been no sound theoretical foundation in terms of learning kernel. This program mainly focuses on a family of multi-kernel algorithms based on convex regularizations. First, we study localized functional complexity to improve previous results of generalization bounds. This enables us to compare the generalization performances of various types of regularizations; Second, we discuss the approximation error under the multi- kernel learning framework, furthermore some specific advantages are illustrated in comparison with single kernel settings; Finally, we concentrate on Multiple Kernel Learning (MKL) algorithms with L^p- regularizer including their associated oracle inequalities and soft sparsity, which seeks the least number of kernels by which the target function can be represented. This study provides theoretical support sufficiently for applicable scopes of multi-kernel learning algorithms, as well as designing new algorithms.

以支持向量机为代表的核方法在机器学习和统计中得到了广泛应用。核机器的表现性能极大的依赖于核函数的选择。针对此问题，近年来出现了许多多核学习方法。然而，对于多核学习至今仍没有完善的理论依据。本文着重研究一类基于凸的正则化项的多核学习算法。首先，深入研究局部复杂度概念以改进已有的泛化界的结果，这使得我们能够比较不同正则化的泛化能力；其次，研究多核背景下的逼近误差，阐明它与单核比较所具有的独特优势；最后，具体研究 L^p-Multiple Kernel Learning 算法的Oracle 不等式以及核系数的软稀疏性，以寻找能表示目标函数的数目相对少的核类。本项目的研究为多核学习算法的适用范围和新多核算法的设计提供充分的理论支持。

机器学习是解决大数据的强有力工具，而再生核方法在机器学习和统计中得到了广泛应用。核机器的表现性能极大的依赖于核函数的选择。针对此问题，近年来出现了许多多核学习方法。然而，对于多核学习至今仍没有完善的理论依据。本文着重研究一类基于凸的正则化项的多核学习算法。首先，深入研究局部复杂度概念以改进已有的泛化界的结果，我的假设条件更与现实相符；其次，研究多核背景下的逼近误差，阐明它与单核比较所具有的独特优势；最后，通过迭代的方式构造核空间，使得我们的算法能捕捉更复杂的数据结构。本项目的研究为多核学习算法的适用范围和新多核算法的设计提供充分的理论支持。主要科研成果可以通过我们的2篇SCI收录的学术论文与一篇在国内核心期刊接收的论文来体现。