PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

An impossibility result for process discrimination
Daniil Ryabko
In: ISIT 2009, June 28 - July 3, 2009, Seoul, South Korea.

Abstract

Two series of binary observations x1; x1; : : : and y1; y2; : : : are presented: at each time n we are given xn and yn. It is assumed that the sequences are generated independently of each other by two stochastic processes. We are interested in the question of whether the sequences represent a typical realization of two different processes or of the same one. We demonstrate that this is impossible to decide in the case when the processes are B-processes. It follows that discrimination is impossible for the set of all (finite-valued) stationary ergodic processes in general. This result means that every discrimination procedure is bound to err with non-negligible frequency when presented with sequences from some of such processes. It contrasts earlier positive results on B-processes, in particular those showing that there are consistent bar d-distance estimates for this class of processes.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:5981
Deposited By:Daniil Ryabko
Deposited On:08 March 2010