Linear pretraining in recurrent mixture density networks

We present a method for pretraining a recurrent mixture density network (RMDN). We also propose a slight modification to the architecture of the RMDN-GARCH proposed by Nikolaev et al. [2012]. The pretraining method helps the RMDN avoid bad local minima during training and improves its robustness to the persistent NaN problem, as defined by Guillaumes [2017], which is often encountered with mixture density networks. Such problem consists in frequently obtaining "Not a number" (NaN) values during training. The pretraining method proposed resolves these issues by training the linear nodes in the hidden layer of the RMDN before starting including non-linear node updates. Such an approach improves the performance of the RMDN and ensures it surpasses that of the GARCH model, which is the RMDN's linear counterpart.