  A new model for generating survival trajectories and data based on applying
an autoencoder of a specific structure is proposed. It solves three tasks.
First, it provides predictions in the form of the expected event time and the
survival function for a new generated feature vector on the basis of the Beran
estimator. Second, the model generates additional data based on a given
training set that would supplement the original dataset. Third, the most
important, it generates a prototype time-dependent trajectory for an object,
which characterizes how features of the object could be changed to achieve a
different time to an event. The trajectory can be viewed as a type of the
counterfactual explanation. The proposed model is robust during training and
inference due to a specific weighting scheme incorporating into the variational
autoencoder. The model also determines the censored indicators of new generated
data by solving a classification task. The paper demonstrates the efficiency
and properties of the proposed model using numerical experiments on synthetic
and real datasets. The code of the algorithm implementing the proposed model is
publicly available.
