Latent variable model for high-dimensional point process with structured
  missingness
Maksim Sinelnikov Manuel Haussmann Harri Lähdesmäki
Longitudinal data are important in numerous fields, such as healthcare,
sociology and seismology, but real-world datasets present notable challenges
for practitioners because they can be high-dimensional, contain structured
missingness patterns, and measurement time points can be governed by an unknown
stochastic process. While various solutions have been suggested, the majority
of them have been designed to account for only one of these challenges. In this
work, we propose a flexible and efficient latent-variable model that is capable
of addressing all these limitations. Our approach utilizes Gaussian processes
to capture temporal correlations between samples and their associated
missingness masks as well as to model the underlying point process. We
construct our model as a variational autoencoder together with deep neural
network parameterised encoder and decoder models, and develop a scalable
amortised variational inference approach for efficient model training. We
demonstrate competitive performance using both simulated and real datasets.