How to sample random game input that looks similar to human control?
A Hidden Markov Model could be useful here. Basically you have a Markov Chain of internal states (e.g. "i just jumped", "i'm running", "i'm ready to jump again") and for each transition of the internal state it generates an action (e.g. "f" or "j") according to a distribution that is different for each internal state. You will need to figure out how many different internal states you need, and then you can learn the model from the data.

If you want to model a bunch of different things inside the hidden state (running/not running, has weapon/doesn't have weapon, ...) you can switch to some kind of recurrent neural net (e.g. LSTM)