Streaming generalized cross entropy

We propose a new method to combine adaptive processes with a class of entropy estimators for the case of streams of data. Starting from a first estimation obtained from a batch of initial data, model parameters are estimated at each step by combining the prior knowledge with the new observation (or a block of observations). This allows to extend the maximum entropy technique to a dynamical setting, also distinguishing between entropic contributions of the signal and the error. Furthermore, it provides a suitable approximation of standard GME problems when the exacted solutions are hard to evaluate. We test this method by performing numerical simulations at various sample sizes and batch dimensions. Moreover, we extend this analysis exploring intermediate cases between streaming GCE and standard GCE, i.e., considering blocks of observations of different sizes to update the estimates, and incorporating collinearity effects as well. The role of time in the balance between entropic contributions of signal and errors is further explored considering a variation of the Streaming GCE algorithm, namely Weighted Streaming GCE. Finally, we discuss the results: In particular, we highlight the main characteristics of this method, the range of application, and future perspectives.