本文为荷兰特文特大学（作者：Eloy Stoppels）的硕士论文，共82页。

本文采用人工神经网络对一级方程式赛车的最终结果进行预测。第16/17赛季的最后四场比赛是根据前17场比赛预测的。本文的第一部分致力于研究人工神经网络的理论基础。目的是让读者了解人工神经网络的术语。通过一些简单的例子，讨论并解释了所有重要的术语。并对其中的一些关键问题进行了更深入的探讨。我们观察多层和多个神经元的影响。我们很清楚为什么要使用深度神经网络。我们讨论的下一个关键方面是“训练人工神经网络”，在训练过程中对自由参数进行了优化。这种优化是通过求解最小化问题来实现的。因此，可以使用最先进的优化方法来训练人工神经网络。另一个关键方面是人工神经网络中使用不同的激活函数和代价函数。最后，我们解释如何使用所谓的正则化方法来避免训练过程中可能出现的错误。第二部分是实验研究。首先，我们给出并解释我们用作预测特征的公共可用数据。然后我们展示了如何初始化人工神经网络，其中展示了多层网络、激活函数等如何影响预测结果。我们使用初始化网络来预测16/17赛季最后四场一级方程式比赛的结果，从而完成实验研究。我们比较了三个不同的数据集，第一个是16/17赛季的实际数据，另外两个是我们以某种方式添加的数据集。其次，将人工神经网络的预测结果与两种简单的预测方法和多类logistic回归进行比较。比较的结论是，使用人工神经网络预测的结果更优越。

In this thesis Artificial Neural Networksare used to predict Formula One finish results. The last four races of theseason 16/17 are predicted based on the first seventeen races. The first partof this thesis is dedicated to the theory behind Artificial Neural Networks.The aim is to give readers insights in the world and terminology of artificialneural networks. All the important terminology is discussed and explained,using some simple examples. Furthermore some key aspect are discussed in moredepth. We look at what the influences of multiple layers and multiple neuronsare. We make clear why a deep neural network is used. The next key aspect wediscuss is; ’training an artificial neural network’. During training the freeparameters are optimized. This optimization is done by solving a minimizationproblem. Therefore, training an artificial neural network can be done by usingstate-of-the-art optimization methods. Other key aspect are the differentactivation functions and cost functions which are used in artificial neuralnetworks. Lastly, we explain how possible errors during training can be avoidedby using so called regularization methods. The second part is dedicated to theexperimental research. First we give and explain public available data which weuse as prediction features. Afterwards we show how to initialize an artificialneural network, where we show how multiple layers, activation functions, etc.influence the predicted results. We finish the experimental research by usingthe initialized network to predict the outcome of the last four Formula Oneraces of the season 16/17. We compare three different data-sets, the first isthe actual data of the season 16/17, the other two are data-sets where we addeddata in a certain way. Next to this, we compare the predicted results of theartificial neural network with two simple prediction methods and with multiclasslogistic regression. The conclusion of this comparison is that using artificialneural networks has benefits as it predicts better outcome results.

1. 引言

2. 文献回顾

3. 人工神经网络

4. 多层多神经元的影响

5. 训练人工神经网络

6. 激活函数

7. 代价函数

8. 正则化

9. 数据准备

10. 不同数据集

11. 结果

12. 如何初始化人工神经网络的解释

13. 一级方程式预测的结果

14. 结论

15. 讨论与未来研究展望

附录A XOR问题

附录B sigmoid激活函数的导数

附录C 双曲tangens激活函数的导数

附录D softmax激活函数的导数

附录E 概率解释

附录F 交叉熵函数的解释

附录G 计算预测比赛结果的示例

更多精彩文章请关注公众号：