Information geometry of U-Boost and Bregman divergence
Information geometry of U-Boost and Bregman divergence
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DOI：
10.1162/089976604323057452
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发表时间：
2004-07-01
影响因子：
2.9
通讯作者：
Eguchi, S
中科院分区：
文献类型：
--
作者：
Murata, N;Takenouchi, T;Eguchi, S
我们的目标是将 AdaBoost 扩展到 U-Boost，在范式中从一组弱学习机器构建更强的分类机器。对由通用凸函数 U 定义的 Bregman 散度的几何理解导致信息几何框架中的 U-Boost 方法扩展到标签集上的有限度量空间。通过考虑域是否受限于概率函数空间，我们提出了两个版本的 U-Boost 学习算法。在顺序步骤中，我们观察到两个相邻的初始分类器通过布雷格曼散度（称为毕达哥拉斯关系）与尺度中的直角三角形相关联。这导致 U-Boost 算法具有温和的收敛特性，如期望最大化算法中所示。对一致性和鲁棒性的统计讨论阐明了基于训练数据随机假设的 U-Boost 方法的属性。
We aim at an extension of AdaBoost to U-Boost, in the paradigm to build a stronger classification machine from a set of weak learning machines. A geometric understanding of the Bregman divergence defined by a generic convex function U leads to the U-Boost method in the framework of information geometry extended to the space of the finite measures over a label set. We propose two versions of U-Boost learning algorithms by taking account of whether the domain is restricted to the space of probability functions. In the sequential step, we observe that the two adjacent and the initial classifiers are associated with a right triangle in the scale via the Bregman divergence, called the Pythagorean relation. This leads to a mild convergence property of the U-Boost algorithm as seen in the expectation-maximization algorithm. Statistical discussions for consistency and robustness elucidate the properties of the U-Boost methods based on a stochastic assumption for training data.