Recently I have become aware of 'likelihood-free' methods being bandied about in literature. However I am not clear on what it means for an inference or optimization method to be likelihood-free.
In machine learning the goal is usually to maximise the likelihood of some parameters to fit a function e.g. the weights on a neural network.
So what exactly is the philosophy of a likelihood-free approach and why do adversarial networks such as GANs fall under this category?