YIG oscillator - where is the oscillator?
The oscillator is the active device, the sustaining device that adds power, with a loop coupled to the YIG sphere tunable resonator in one terminal, to control its frequency of oscillation. 

Device parasitics which are not shown (but would have to be used in any simulation, and considered in any explanation) complete the oscillator. For instance, in the third circuit with the gate-connected YIG, The Cdg parasitic is a vital part of the oscillator, making it rather Clapp-Colpitts, if you consider the coupling to the YIG as a series connected LC.

Wikipedia is not that encyclopedic on RF engineering, it doesn't give an exhaustive list of available RF oscillator configurations.