  We discuss deep learning inference for the neutron star equation of state
(EoS) using the real observational data of the mass and the radius. We make a
quantitative comparison between the conventional polynomial regression and the
neural network approach for the EoS parametrization. For our deep learning
method to incorporate uncertainties in observation, we augment the training
data with noise fluctuations corresponding to observational uncertainties.
Deduced EoSs can accommodate a weak first-order phase transition, and we make a
histogram for likely first-order regions. We also find that our observational
data augmentation has a byproduct to tame the overfitting behavior. To check
the performance improved by the data augmentation, we set up a toy model as the
simplest inference problem to recover a double-peaked function and monitor the
validation loss. We conclude that the data augmentation could be a useful
technique to evade the overfitting without tuning the neural network
architecture such as inserting the dropout.
