Optimum transport (OT) idea describes normal ideas to outline and choose, amongst many alternatives, probably the most environment friendly method to map a likelihood measure onto one other. That idea has been largely used to estimate, given a pair of supply and goal likelihood measures , a parameterized map that may effectively map onto . In lots of purposes, resembling predicting cell responses to remedies, the info measures (options of untreated/handled cells) that outline optimum transport issues don’t come up in isolation however are related to a context (the therapy). To account for and incorporate that context in OT estimation, we introduce CondOT, an strategy to estimate OT maps conditioned on a context variable, utilizing a number of pairs of measures tagged with a context label . Our objective is to be taught a world map which isn’t solely anticipated to suit all pairs within the dataset , i.e., , however ought to generalize to provide significant maps conditioned on unseen contexts . Our strategy harnesses and supplies a novel utilization for {em partially enter convex neural networks}, for which we introduce a sturdy and environment friendly initialization technique impressed by Gaussian approximations. We exhibit the flexibility of CondOT to deduce the impact of an arbitrary mixture of genetic or therapeutic perturbations on single cells, utilizing solely observations of the consequences of mentioned perturbations individually.
