Learning of Bayesian Neural Networks and Their Applications to Hidden Markov Chain

贝叶斯神经网络的学习及其在隐马尔可夫链中的应用

• 批准号: 17500153
• 负责人: ITO Yoshifusa
• 金额: $ 2.18万
• 依托单位: Aichi Gakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17500153/
• 关键词: Neural network; Hidden Markov chain; Bayesian decision; ベイズ判別関数; 三層神経回路網; 学習; ベイズ神経回路網; 判別関数; 関数近似; 多項式

The goal of this research was to develop a sophisticated neural network which can learn the Bayesian discriminant function and, to use it to estimate the hidden Markov chain. The results we have obtained during the period of the research supported by the Grant-in-Aid for Scientific Research c can be summarized into three points.1. The three layer neural network, which may learn a Bayesian discriminant function, had been proposed before we started the present work. However, it had difficulty in learning. As it is a general belief that a neural network having fewer units can learn better, we first tried to decrease the hidden units. We have theoretically proved that the small number of the hidden units of our network is actually the minimum.2.In the rase where the probability distributions are simple, this network, having the minimum number of hidden units, can be used for estimating the hidden Markov chain. When this network is equipped with parameter units, it can learn simultaneously several Bayesian discriminant functions respectively corresponding to the several states of the hidden Markov chain.3.However, the network cannot learn the dicriminant functions in general cases. The reason is that learning with dichotomous teacher signals is difficult. So we constructed a new type of neural network, where the degree of freedom of the hidden units is limited. Though this inevitably causes an increment of hidden units, the network performs better The theory is stated in a paper which is now in printing, and the simulation results have been presented at a domestic and several international conferences.Thus, when the probability distributions are simple the network can estimate the hidden Markov chains. Even in general cases, the recent results are promising.

这项研究的目的是开发一个复杂的神经网络，该网络可以学习贝叶斯判别功能，并使用它来估计隐藏的马尔可夫链。我们在科学研究C赠款支持的研究期间获得的结果可以汇总为三点。1。在我们开始本工作之前，已经提出了可能学习贝叶斯判别功能的三层神经网络。但是，它很难学习。由于普遍认为，具有更少单位的神经网络可以学习得更好，因此我们首先试图减少隐藏单位。从理论上讲，我们已经证明了我们网络的隐藏单元的少量数量实际上是最小值。2。在概率分布很简单的RASE中，该网络具有最小的隐藏单元数量，可用于估算隐藏的Markov链。当该网络配备了参数单元时，它可以同时学习与隐藏马尔可夫链的多个状态相对应的几个贝叶斯判别函数。原因是很难使用二分教师信号学习。因此，我们构建了一种新型的神经网络，其中隐藏单元的自由度受到限制。尽管这不可避免地会导致隐藏单元的增加，但网络的执行效果更好，该理论在现在正在打印的论文中说明，并且在国内和几个国际会议上呈现了模拟结果。当概率分布很简单时，网络可以估计隐藏的马尔可夫链。即使在一般情况下，最近的结果也很有希望。

项目成果

Learning of neural networks with dichotomic random teacher signals

使用二分随机教师信号学习神经网络

• 发表时间: 2007
• 作者: Yoshifusa Ito;Cidambi Srinivasan;Hiroyuki Izumi
• 通讯作者: Hiroyuki Izumi

Learning of Bayesian discriminant functions by $a$ layered neural network

通过$a$分层神经网络学习贝叶斯判别函数

• 发表时间: 2007
• 作者: Yoshifusa Ito;Cidambi Srinivasan;Hiroyuki Izumi
• 通讯作者: Hiroyuki Izumi

2値乱数による神経回路網の学習とベイズ判別関数学習への応用

使用二进制随机数学习神经网络及其在贝叶斯判别函数学习中的应用

• 发表时间: 2007
• 作者: 伊藤嘉房;キダンビ スリニヴァサン;泉寛幸
• 通讯作者: 泉寛幸

Bayesian decision theory on three-layer neural networks

三层神经网络的贝叶斯决策理论

• 发表时间: 2005
• 期刊: Neurocomputing 63
• 作者: Yoshifusa Ito;Cidambi Srinivasan
• 通讯作者: Cidambi Srinivasan

Simultaneous approximation of polynomials and derivatives and their applications to neural networks

多项式和导数的同时逼近及其在神经网络中的应用

• 发表时间: 2008
• 期刊: Neural Computation 20(ゲラ刷りによる)
• 作者: WATANABE Takesato;YAMAGUCHI Koji;KUDO Kazuo;KAWASAKI Yoshinori;NOHARA Hitoshi;Yoshifusa Ito,
• 通讯作者: Yoshifusa Ito,