TY - JOUR

T1 - Predicting non-stationary processes

AU - Ryabko, Daniil

AU - Hutter, Marcus

PY - 2008/5

Y1 - 2008/5

N2 - Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences. Consider the question of when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain sense), if one of the measures is chosen to generate the sequence. This question may be considered a refinement of the problem of sequence prediction in its most general formulation: for a given class of probability measures, does there exist a measure which predicts all of the measures in the class? To address this problem, we find some conditions on local absolute continuity which are sufficient for prediction and generalize several different notions that are known to be sufficient for prediction. We also formulate some open questions to outline a direction for finding the conditions on classes of measures for which prediction is possible.

AB - Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences. Consider the question of when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain sense), if one of the measures is chosen to generate the sequence. This question may be considered a refinement of the problem of sequence prediction in its most general formulation: for a given class of probability measures, does there exist a measure which predicts all of the measures in the class? To address this problem, we find some conditions on local absolute continuity which are sufficient for prediction and generalize several different notions that are known to be sufficient for prediction. We also formulate some open questions to outline a direction for finding the conditions on classes of measures for which prediction is possible.

KW - Absolute/KL divergence

KW - Average/expected criteria

KW - Local absolute continuity

KW - Mixtures of measures

KW - Non-stationary measures

KW - Sequence prediction

UR - http://www.scopus.com/inward/record.url?scp=41149139797&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2007.04.004

DO - 10.1016/j.aml.2007.04.004

M3 - Article

SN - 0893-9659

VL - 21

SP - 477

EP - 482

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 5

ER -