MARS vs. CART regression predictive power

Question

I have been wondering recently about the prediction power of the two similar models: Decision Trees and the MARS model (instead of fitting the mean to the subsets, OLS line is estimated). Given that in regression we're usually dealing with continous data, is any of them superior to one another when it comes to actual forecasting? My intuition is, that if the best possible fit is the mean, then MARS will simply estimate $\hat y=0x+const$. So basically MARS can estimate everything that CART can, and CART cannot estimate everything that MARS can.

Can you safely say, that MARS is a superior algorithm to CART? Or am I missing something?

If so, has any research on combining MARS with some more complex algorithm such as for example XGBoost been done?

Answer 1

CART will also estimate the constant function in the example you cite. The advantage of MARS comes from the fact that it creates continuous functions, which are typically a more realistic estimator than discontinuous piecewise-constant functions. The advantage of CART is piecewise-constant functions are simple and extremely fast to compute.