Before revision:  Numerical results show that these two methods are accurate and reliable and improve the results of the GPR-MC method in handling American options on very large baskets of assets  .
After revision:  Numerical results show that these two methods are accurate and reliable and improve the results of the GPR-MC method in handling American options on very large baskets of assets . Moreover we also consider the rough Bergomi model, which provides stochastic volatility with memory. Despite this model is only bidimensional, the whole history of the process impacts on the price, and handling all this information is not obvious at all. To this aim, we present how to adapt the GPR-Tree and GPR-EI methods and we focus on pricing American options in this non-Markovian framework .