Optimal transport (OT) theory describes the general principles for defining and selecting, among many possible options, the most efficient way to map one probability measure onto another. That theory has been used primarily to estimate, given a pair of origin and destination probability measures. a parameterized map which can efficiently map upon . In many applications, such as predicting cellular responses to treatments, the data measure (characteristics of untreated/treated cells) that define optimal transport problems do not arise in isolation, but are associated with a context (the treatment). To take into account and incorporate that context in the OT estimation, we present CondOT, an approach to estimate OT maps conditional on a context variable, using several pairs of measures. tagged with a context tag . Our goal is to learn a global Map that is not only expected to fit all pairs in the data set that is to say, but should generalize to produce meaningful maps conditioned in invisible contexts . Our approach leverages and provides novel use for partially convex input neural networks, for which we present a robust and efficient initialization strategy inspired by Gaussian approximations. We demonstrate the ability of CondOT to infer the effect of an arbitrary combination of genetic or therapeutic perturbations on individual cells, using only observations of the effects of such perturbations separately.
