The engineering of multispecies microbial communities is important to applications in healthcare, biotechnology, and environmental sustainability. Predicting the structures of such communities requires knowledge of the interactions between the species involved. When high-order interactions are present, bottom-up approaches, which rely on the assembly of all possible subcommunities, become prohibitive because the number of such subcommunities scales exponentially with the number of species. Here, we present an alternative, top-down approach, EPICS, which requires the assembly of subcommunities whose number scales linearly with the number of species, hugely reducing experimental effort. EPICS estimates effective pairwise interactions between species, which subsume high-order interactions, using data from monocultures and leave-one-out subcommunities and predicts community structures. The method is efficient and scalable to large communities.