Before revision:  We provide an approach based on identifying carefully chosen features of the streamwhich allows linear regression to be used to characterise the functional relationship between  explanatory variables and the conditional distribution of the response;
After revision:  A certain graded feature set of a stream, known in the rough path literature as the signature, has a universality that allows formally, linear regression to be used to characterise the functional relationship between explanatory variables and the conditional distribution of the response;