Stochastic complexities of reduced rank regression in Bayesian estimation
Stochastic complexities of reduced rank regression in Bayesian estimation
复制标题
DOI：
10.1016/j.neunet.2005.03.014
复制
发表时间：
2005-09-01
期刊：
影响因子：
7.8
通讯作者：
Watanabe, S
中科院分区：
文献类型：
--
作者：
Aoyagi, M;Watanabe, S
降序回归从输入输出对的示例中提取基本信息。它可以理解为具有线性隐藏单元的三层神经网络。然而，降阶近似是一种非正则统计模型，具有简并的Fisher信息矩阵。即使在统计学中，它的泛化误差也是未知的。在本文中，我们基于学习机奇点的解析，给出了贝叶斯估计中泛化误差的精确渐近形式。为此，计算学习理论的 zeta 函数的最大极点。我们提出了一种新的递归放大方法，它可以实现降阶近似的完全去奇异化。 (c) 2005 Elsevier Ltd. 保留所有权利。
Reduced rank regression extracts an essential information from examples of input-output pairs. It is understood as a three-layer neural network with linear hidden units. However, reduced rank approximation is a non-regular statistical model which has a degenerate Fisher information matrix. Its generalization error had been left unknown even in statistics. In this paper, we give the exact asymptotic form of its generalization error in Bayesian estimation, based on resolution of learning machine singularities. For this purpose, the maximum pole of the zeta function for the learning theory is calculated. We propose a new method of recursive blowing-ups which yields the complete desingularization of the reduced rank approximation. (c) 2005 Elsevier Ltd. All rights reserved.