Predicting Non-Stationary Processes

Daniil Ryabko (1) , Marcus Hutter (2)

1 SEQUEL - Sequential Learning
2 ANU - Australian National University - Department of engineering

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.

Mots clés: Sequence prediction; Local absolute continuity; Non-stationary measures; Average/expected criteria; Absolute/KL divergence; Mixtures of measures

Domaines: Apprentissage [cs.LG]; Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Daniil Ryabko, Marcus Hutter. Predicting Non-Stationary Processes. Applied Mathematics Letters, 2008, 21 (5), pp.477-482. ⟨10.1016/j.aml.2007.04.004⟩. ⟨hal-00639573⟩