基于贝叶斯神经网络的非参数回归

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。

Bayesian Neural Network for Nonparametric Regression

With neural networks, the main difficult in improving the model generalization capability is controlling the complexity of the model. This paper investigates a Bayesian neural network learning for nonparametric regression. Prior knowledge about the model parameters can be incorporated within Bayesian inference and combined with training data to control complexity of different parts of the model. A Markov chain Monte Carlo algorithm is used to optimize model control parameters and obtain the predictive distribution. We show that the complexity of the models adapts to the complexity of the data and produces good results on five noisy test functions in two dimension. The performance and advantage of this approach are compared with conventional neural network methods.