Sorry, nothing definite yet. Any sort of tree-based computation which makes early pruning decision is more efficient than full matrix multiplication, even if matrix is sparse. Then, high-order computation like power is again more efficient than simple linear model. Those two directions are quite probable.
Reminds me of the "Expert Systems" from the 1980s. They saw similar levels of (inflation-adjusted) hype too. Decision trees have had their heyday; wonder if they'll be back in fashion soon.
