Online Prediction For Streaming Observational Data

Abstract: The automated collection of streaming observational data has become standard and defies most traditional analytic techniques. It is not just that models are hard to identify, there may not be any model that can be safely and usefully assumed. Indeed, frequently it is only predictions that can be made and assessed. Problems for this kind of data are often called {\cal{M}}-Open and have motivated new approaches and philosophies. This paper will review some of the most successful recent predictive methods for the {\cal{M}}-Open problem class. Techniques include predictors using expert advice such as the Shtarkov solution, Bayesian nonparametrics such as Gaussian process priors, hash function based predictors such as the {\sf Count-Min} sketch, and conformal prediction. Throughout, the properties of the predictors are presented and compared from a principled standpoint.