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提高神经网络模型推广能力的关键是控制模型的复杂度。该文探索了贝叶斯神经网络的非参数回归的建模方法,通过融入模型参数的先验知识,在给定数据样本及模型假设下进行后验概率的贝叶斯推理,使用马尔可夫链蒙特卡罗算法来优化模型控制参数,实现了对神经网络模型中不同部分复杂度的控制,获得了模型参数的后验分布及预测分布。在5个含噪二维函数回归问题上的应用显示了模型的复杂度能根据数据的复杂度而自适应调整,并给出了较好的预测结果。
The key to improve the ability of neural network model to promote is to control the complexity of the model. This paper explores the modeling method of non-parametric regression of Bayesian neural network. By incorporating prior knowledge of model parameters, Bayesian inference of posterior probability is given under given data samples and model assumptions, Chain Monte Carlo algorithm to optimize the model control parameters to achieve the control of the complexity of different parts of the neural network model to obtain the posterior distribution of model parameters and prediction distribution. The application of five noisy two-dimensional function regression problems shows that the complexity of the model can be adaptively adjusted according to the complexity of the data and gives a good prediction result.