Mammalian central nervous system (CNS) neurons regrow their axons poorly following injury, resulting in irreversible functional losses. Identifying therapeutics that encourage CNS axon repair has been difficult, in part because multiple etiologies underlie this regenerative failure. This suggests a particular need for drugs that engage multiple molecular targets. Although multitarget drugs are generally more effective than highly selective alternatives, we lack systematic methods for discovering such drugs. Target-based screening is an efficient technique for identifying potent modulators of individual targets. In contrast, phenotypic screening can identify drugs with multiple targets; however, these targets remain unknown. To address this gap, we combined the two drug discovery approaches using machine learning and information theory. We screened compounds in a phenotypic assay with primary CNS neurons and also in a panel of kinase enzyme assays. We used learning algorithms to relate the compounds' kinase inhibition profiles to their influence on neurite outgrowth. This allowed us to identify kinases that may serve as targets for promoting neurite outgrowth as well as others whose targeting should be avoided. We found that compounds that inhibit multiple targets (polypharmacology) promote robust neurite outgrowth in vitro. One compound with exemplary polypharmacology was found to promote axon growth in a rodent spinal cord injury model. A more general applicability of our approach is suggested by its ability to deconvolve known targets for a breast cancer cell line as well as targets recently shown to mediate drug resistance.