  Probabilistic machine learning techniques can learn both complex relations
between input features and output quantities of interest as well as take into
account stochasticity or uncertainty within a data set. In this initial work,
we explore the use of one such probabilistic network, the Mixture Density
Network (MDN), to reproduce fission yields and their uncertainties. We study
mass yields for the spontaneous fission of $^{252}$Cf, exploring the number of
training samples needed for converged predictions, how different levels of
uncertainty propagate from the training set to the MDN predictions, and how
well physical constraints of the yields - such as normalization and symmetry -
are upheld by the algorithm. Finally, we test the ability of the MDN to
interpolate between and extrapolate beyond samples in the training set using
energy-dependent mass yields for the neutron-induced fission on $^{235}$U. The
MDN provides a reliable way to include and predict uncertainties and is a
promising path forward for supplementing sparse sets of nuclear data.
