Approximations

technically all prediction methods are approximations of Solomonoff Induction

Use a Turing machine that halts (lose all non-halting explanations)

Use randomness and select a subset of all hypotheses. i.e. Monte Carlo method. Perhaps use an evolutionary algorithm that that starts with seed hypotheses and vary the ones that get closest to the observation

Jurgen Schmidhuber equates faster algorithms with high probability, and uses that to create a very fast approximation. But the assumption that faster algorithms are more likely isn’t a given.