content_image/301083.jpg
<img src='content_image/301083.jpg'>

training rate helps to prevent suboptimal convergence. The second panel in Fig. 6 shows that validation precision generally follows the behaviour of training precision at a lower level. 

## 6.1. Predicting the Next Event 

Table 3 shows our results and a comparison to the best result presented by Breuker et al. (2016). The table shows that our RNN approach surpasses the per- formance of probabilistic finate automatons on many datasets. For the BPI 2013 Incidents data, the BPI 2012 A, and the BPI 2012 O subsets, our training and vali- dation precision values are above the best values reported by Breuker et al. (2016). For the BPI 2013 Problems dataset, our approach offers better training precision, but the validation precision is lower than that reported by Breuker et al. (2016), and on the BPI 2012 W dataset, our approach performs poorly. Overall, this is in line with the expectations based on mutual information (Sec. 3.5) which showed that both PFA and RNN should be able to model our process data equally well. 

Comparing the training and validation precision shows that little overfitting occurs, with the validation precision generally within ± 0 . 05 of the training precision. The standard deviations for the validation precision are an order of magnitude above those for the training sample because of the smaller size of the validation sample 

