General regression in cloud computing

Regression is one of the approach/technology of machine learning. This technology is used in a situation where we want to estimate from input parameters the scalar quantity. In practice we often face with situation where due to deficient computing resources, we are not able to train required function (in sense the minimum error). This phenomenon can cause a various factors (e.g. large number of training data, high degree of training function ...). An interesting question is: how helpful is cloud computing in this situation.