  While thousands of exoplanets have been confirmed, the known properties about
individual discoveries remain sparse and depend on detection technique. To
utilize more than a small section of the exoplanet dataset, tools need to be
developed to estimate missing values based on the known measurements. Here, we
demonstrate the use of a neural network that models the density of planets in a
space of six properties that is then used to impute a probability distribution
for missing values. Our results focus on planetary mass which neither the
radial velocity nor transit techniques for planet identification can provide
alone. The neural network can impute mass across the four orders of magnitude
in the exoplanet archive, and return a distribution of masses for each planet
that can inform about trends in the underlying dataset. The average error on
this mass estimate from a radial velocity detection is a factor of 1.5 of the
observed value, and 2.7 for a transit observation. The mass of Proxima Centauri
b found by this method is $1.6^{\rm +0.46}_{\rm -0.36}$ M$_\oplus$, where the
upper and lower bounds are derived from the root mean square deviation from the
log mass probability distribution. The network can similarly impute the other
potentially missing properties, and we use this to predict planet radius for
radial velocity measurements, with an average error of a factor 1.4 of the
observed value. The ability of neural networks to search for patterns in
multidimensional data means that such techniques have the potential to greatly
expand the use of the exoplanet catalogue.
