# Randomness Assumption (IID assumption)

The randomness assumption (also known as the IID assumption) is that the observations in a sequence are generated independently from the same probability distribution on the space of possible observations (often ). A weaker (for a wide class of , according to de Finetti's theorem) assumption is that of exchangeability.

The randomness assumption is used in stochastic prediction and conformal prediction. It is a standard assumption in machine learning. In applications, algorithms developed under this assumption (such as SVM) are often applied when the assumption is violated. However, if the observations , , are coming from a stationary measure on , the IID assumption can be often made "almost satisfied" by extending the objects . For example, in the case of time series we may add the pre-history of to (and this will work very well if the time series is Markov).