Mistnet is an R package that produces probability densities over multivariate outcomes. Ecologists can use it to define probability densities over possible species assemblages, as described in this paper I wrote for Methods and Ecology and Evolution.
Mistnet models are stochastic neural networks, meaning that they include stochastic latent variables (like random effects) that account for correlations among the outcome variables that cannot be explained by the inputs.
The model uses a Generalized Expectation Maximization approach to model fitting (maximized penalized likelihood), as described in this paper from Tang and Salakhutdinov at NIPS 2013 and in the Methods paper referred to above.