贝叶斯神经网络建模预测方法及其应用

Modeling & predictive method of Bayesian neural network

针对神经网络建模时,其模型的复杂性难以控制而且缺乏分析结果的工具,以及贝叶斯方法可以通过定义一些超参数的模糊先验来控制模型参数复杂性,并且可对任何感兴趣的变量产生后验预测分布,使得置信区间的计算成为可能。研究了贝叶斯神经网络的建模预测问题,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。通过动调陀螺仪漂移数据建模应用分析结果证明此方法可以达到较好的建模预测效果。

With neural networks, the main difficulty in model building is controlling the complexity of the model and lack of tools for analyzing the results, such as confidence interval. However, Bayesian approach can handle such problems by defining vague priors for the hyperparameters that determine the model complexity. And the Bayesian analysis yields posterior predictive distributions for any variables of interest, making the computation of confidence intervals possible. Prior knowledge about the model parameters can be incorporated in Bayesian inference and combined with training data to control complexity of different parts of the model. Markov chain Monte Carlo method is applied to optimize the model control parameters and obtain the predictive distribution. The Bayesian neural network method is studied and used in the drift modeling for gyroscopes. Results show that the Bayesian neural network can produce better modeling and predictive performance.