Learning in Nonstationary Environments: A Survey

The prevalence of mobile phones, the internet-of-things technology, and networks of sensors has led to an enormous and ever increasing amount of data that are now more commonly available in a streaming fashion [1]-[5]. Often, it is assumed - either implicitly or explicitly - that the process generating such a stream of data is stationary, that is, the data are drawn from a fixed, albeit unknown probability distribution. In many real-world scenarios, however, such an assumption is simply not true, and the underlying process generating the data stream is characterized by an intrinsic nonstationary (or evolving or drifting) phenomenon. The nonstationarity can be due, for example, to seasonality or periodicity effects, changes in the users' habits or preferences, hardware or software faults affecting a cyber-physical system, thermal drifts or aging effects in sensors. In such nonstationary environments, where the probabilistic properties of the data change over time, a non-adaptive model trained under the false stationarity assumption is bound to become obsolete in time, and perform sub-optimally at best, or fail catastrophically at worst.