20 research outputs found
An impossibility result for process discrimination
Two series of binary observations and are
presented: at each time we are given and . It is assumed
that the sequences are generated independently of each other by two
B-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 sense that every
discrimination procedure is bound to err with non-negligible frequency when
presented with sequences from some B-processes. This contrasts earlier positive
results on B-processes, in particular those showing that there are consistent
-distance estimates for this class of processes
Guessing Revisited: A Large Deviations Approach
The problem of guessing a random string is revisited. A close relation
between guessing and compression is first established. Then it is shown that if
the sequence of distributions of the information spectrum satisfies the large
deviation property with a certain rate function, then the limiting guessing
exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the
rate function. Other sufficient conditions related to certain continuity
properties of the information spectrum are briefly discussed. This approach
highlights the importance of the information spectrum in determining the
limiting guessing exponent. All known prior results are then re-derived as
example applications of our unifying approach.Comment: 16 pages, to appear in IEEE Transaction on Information Theor