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贝叶斯框架下广义结合泛函网络与广义约束神经网络的研究与应用
其他题名Generalized Associativity Functional Networks and Generalized Constraint Neural Networks under Bayesian Framework
曲寒冰
学位类型工学博士
导师胡包钢
2007-06-01
学位授予单位中国科学院研究生院
学位授予地点中国科学院自动化研究所
学科专业模式识别与智能系统
关键词变分贝叶斯逼近 广义结合泛函网络 广义约束神经网络 半参数模型 植物生长建模 Variational Bayes Approximation Generalized Associativity Functional Networks Generalized Constraint Neural Networks Semi-parametric Model Plant Growth Modelling
中文摘要广义结合泛函网络(Generalized Associativity Functional Networks)是一种典型的泛函网络模型,它可以在设计模型时首先考虑存在的领域知识,然后再对参数进行学习。但是在对其参数进行学习时,由于模型参数存在着等式约束,这样就无法直接估计后验概率分布。本文首先利用参数变换的方法消除等式约束,然后再利用变分贝叶斯逼近的方法对后验概率进行逼近。本文的主要的工作包括以下几个方面: 1.提出了一种参数存在等式约束的变分贝叶斯逼近的方法,并将其用于估计广义结合泛函网络模型参数的后验概率。当模型参数存在线性等式约束和线性不等式的情况时,首先通过线性变换的方法消除泛函网络参数的约束,然后再利用变分贝叶斯逼近方法对模型参数的后验概率进行估计。这种方法被应用于广义约束泛函网络之后,分别对混沌、线性与非线性时间序列进行了分析和预测。在分析混沌时间序列时,变分贝叶斯可以提供参数的后验概率,这给参数的统计推断带来了很大的方便,而在利用贝叶斯广义泛函网络队自回归模型进行模型选择时,变分自由能量可以作为一种准则来进行模型选择。而且在太阳黑子预测这样的实际问题上,贝叶斯广义结合泛函网络也体现其可比性与优越性; 2.提出了一种具有广义约束意义的神经网络模型――广义约束神经网络(Generalized Constraint Neural Networks),并研究了其中两种具有代表性的模型――加和模型和乘积模型的基本特性。针对建模中可能出现的各种先验知识,我们从模型结构的角度出发,考虑如何将先验信息引入到神经网络系统设计之中,进而引出了广义约束神经网络的参数可辨识性问题和奇异点问题。实验表明,在某些情况下,先验模型的引入可以提高模型的泛化能力,并可以有条件地对模型中据有物理意义的参数进行估计。虽然乘积模型可能会出现奇异点问题,但是对于揭示模型的物理特性,这样的发现具有一定的积极意义; 3.基于广义约束神经网络的加和模型,将参数模型和非参数模型进行结合,对实际的温室植物数据进行了生态建模,在实现植物生长预测的同时,有效地估计了植物生长过程中的温度阈值参数。在对具有加和形式的广义约束神经网络进行学习时,将基于变分贝叶斯逼近的Bayesian Backfitting方法引入其中,在贝叶斯框架下对模型的参数进行了估计。对于生态模型系统来说,一般都存在着大量的先验信息,我们提出的具有半参数形式的约束神经网络模型对于如何将先验信息引入到系统建模之中,作了具有积极意义的研究与探讨,虽然在预测性能上与纯神经网络相比稍差,但是却可以通过参数化模型获得一些在物理上具有一定意义的参数,在提高预测精度的前提下,提高了模型的可解释性。
英文摘要Prior knowledge is any information obtained from previous experience or data, and it can be represented as initial structure of model and the range of parameters while building models. In this work, we mainly discuss how to incorporate different prior knowledge into neural networks for the building of models. First, functional networks are introduced and studied for the reason that they can reproduce some physical and engineering properties to corresponding structure in a natural way. Thereafter, we propose a constraint neural networks which aim at the associating of neural networks and partially known relationships, and then apply this model to a real-world problems Though many methods have been proposed for the learning of functional networks and constraint neural networks, they are mainly based on maximum-likelihood(ML) or maximum a posterior (MAP) schemes. Bayesian methodology has a number of virtues in comparison with ML and MAP, e.g. the prior knowledge can be easily incorporated in a coherent way and Bayesian approach prevents overfitting problem naturally. In this thesis, we mainly study the the properties of functional networks (mainly generalized associativity functional networks-GAFN) and constraint neural networks(mainly superposition case) under the Bayesian framework, and propose a variational Bayes method to approximate the posterior distribution over parameters of the functional networks and constraint neural networks. The main contributions of this thesis include following issues: 1.We propose a variational learning method to approximate the posterior distribution over parameters of the generalized associative functional networks under the Bayesian framework. By use of linear transformation, the equality constraints on the parameters are eliminated and the approximation to the posterior is restricted within a subspace of the parameters. Furthermore, a variational approximation for parameter with inequality constraints is also studied. 2.We bring forward generalized constraint neural networks for the purpose of associating neural networks with partially known relationships. Two typical cases - Superposition and Multiplication, are studied to discovery the basic characteristics of constraint neural networks. The identifiability of parameters and the singularity problem are introduced during the applications of this model. 3.Based on the generalized constraint neural networks, the parametric model and neural networks are combined to build the ecological model of the plant growth process. A lot of meaningful discussions have been made for the application of semi-parametric methods. We also developed a nonlinear function with respect to the threshold temperature, and applied this method to the parametric model in the constraint neural networks.
馆藏号XWLW1070
其他标识符200318014603021
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/5992
专题毕业生_博士学位论文
推荐引用方式
GB/T 7714
曲寒冰. 贝叶斯框架下广义结合泛函网络与广义约束神经网络的研究与应用[D]. 中国科学院自动化研究所. 中国科学院研究生院,2007.
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