  Dose-response prediction in cancer is an active application field in machine
learning. Using large libraries of \textit{in-vitro} drug sensitivity screens,
the goal is to develop accurate predictive models that can be used to guide
experimental design or inform treatment decisions. Building on previous work
that makes use of permutation invariant multi-output Gaussian Processes in the
context of dose-response prediction for drug combinations, we develop a
variational approximation to these models. The variational approximation
enables a more scalable model that provides uncertainty quantification and
naturally handles missing data. Furthermore, we propose using a deep generative
model to encode the chemical space in a continuous manner, enabling prediction
for new drugs and new combinations. We demonstrate the performance of our model
in a simple setting using a high-throughput dataset and show that the model is
able to efficiently borrow information across outputs.
