Not mainstream, but there is something called Random Ferns (technically a mix of Naive Bayes and Random Forest) which is even faster than Random Forest because

Not mainstream, but there is something called Random Ferns (technically a mix of Naive Bayes and Random Forest) which is even faster than Random Forest because it optimizes nothing and has almost no conditional jumps both in training and prediction codes. The accuracy is usually a bit worse, but the difference seems to decrease with the hardness of a problem.