Generic Bounds on the Maximum Deviations in Sequential Prediction: An Information-Theoretic Analysis
This work provides theoretical limits for sequential prediction, which is incremental as it builds on information-theoretic analysis to address uncertainty in prediction tasks.
The paper tackles the problem of bounding maximum deviations in sequential prediction errors by deriving fundamental bounds that depend solely on the conditional entropy of the data, showing that these bounds are asymptotically achieved if and only if the prediction error is white and uniformly distributed.
In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data point to be predicted given the previous data points. In the asymptotic case, the bounds are achieved if and only if the prediction error is white and uniformly distributed.