We decomposed density functional theory charge densities of 53 nitroaromatic molecules into atom-centered electric multipoles using the distributed multipole analysis that provides a detailed picture of the molecular electronic structure. Three electric multipoles, (the charge of the nitro groups), (the total dipole, i.e., polarization, of the nitro groups), (the total electron delocalization of the C ring atoms), and the number of explosophore groups (#NO2) were selected as features for a comprehensive machine learning (ML) investigation. The target property was the impact sensitivity h50 (cm) values quantified by drop-weight measurements, with a large h50 (e.g., 150 cm) indicating that an explosive is insensitive and vice versa. After a preliminary screening of 42 ML algorithms, four were selected based on the lowest root mean square errors: Extra Trees, Random Forests, Gradient Boosting, and AdaBoost. Compared to experimental data, the predicted h50 values of molecules having very different sensitivities for the four algorithms have differences in the range 19-28%. The most important properties for predicting h50 are the electron delocalization in the ring atoms and the polarization of the nitro groups with averaged weights of 39% and 35%, followed by the charge (16%) and number (10%) of nitro groups. A significant result is how the contribution of these properties to h50 depends on their actual sensitivities: for the most sensitive explosives (h50 up to ∼50 cm), the four properties contribute to reducing h50, and for intermediate ones (∼50 cm ≲ h50 ≲ 100 cm) #NO2 and contribute to increasing it and the other two properties to reducing it. For highly insensitive explosives (h50 ≳ 200 cm), all four properties essentially contribute to increasing it. These results furnish a consistent molecular basis of the sensitivities of known explosives that also can be used for developing safer new ones.