We compare the full waveform inversion (FWI), skeletonized wave equation inversion (SWI), and supervised Machine Learning (ML) algorithms with one another. For velocity inversion the advantage of SWI over FWI is it is more robust and has less of a tendency in getting stuck at local minima. This is because SWI only needs to explain the kinematic information in the seismograms, which is less demanding than FWI’s difficult task of explaining all of the wiggles in every arrival. The disadvantage of SWI is that it provides a tomogram with theoretically less resolution than the ideal FWI tomogram. In this case, the SWI tomogram can be used as an excellent starting model for FWI. SWI is similar to supervised Machine Learning in that both use skeletonized representations of the original data. Simpler input data lead to simpler misfit functions characterized by quicker convergence to useful solutions. I show how a hybrid ML+SWI method and the implicit function theorem can be used to extract almost any skeletal feature in the data and invert it using the wave equation. This assumes that the skeletal data are sensitive to variations in the model parameter of interest.