Diffusion Kernels on Statistical Manifolds
Diffusion Kernels on Statistical Manifolds
复制标题
DOI：
--
复制
发表时间：
2005-12
期刊：
影响因子：
--
通讯作者：
J. Lafferty;Guy Lebanon
中科院分区：
文献类型：
--
作者：
J. Lafferty;Guy Lebanon
介绍了一类利用统计模型几何结构进行统计学习的核函数。该核基于与统计族相关的Fisher信息度量定义的黎曼流形上的热方程，推广了欧氏空间的高斯核。作为一种重要的特例，导出了基于多项式族几何的核，从而得到了自然适用于离散数据的基于核的学习算法。利用黎曼流形上拉普拉斯算子的特征值的界，证明了核的复盖数和Rademacher平均的界。给出了文档分类的实验结果，对于文档分类，多项式几何的使用是自然的和良好的动机，并且比标准使用的高斯或线性核获得了改进，后者已经成为文本分类的标准。
A family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. The kernels are based on the heat equation on the Riemannian manifold defined by the Fisher information metric associated with a statistical family, and generalize the Gaussian kernel of Euclidean space. As an important special case, kernels based on the geometry of multinomial families are derived, leading to kernel-based learning algorithms that apply naturally to discrete data. Bounds on covering numbers and Rademacher averages for the kernels are proved using bounds on the eigenvalues of the Laplacian on Riemannian manifolds. Experimental results are presented for document classification, for which the use of multinomial geometry is natural and well motivated, and improvements are obtained over the standard use of Gaussian or linear kernels, which have been the standard for text classification.