Comprehensive lower bounds on sequential prediction
Author
Vanlı, N. Denizcan
Sayın, Muhammed O.
Ergüt, S.
Kozat, Süleyman S.
Date
2014-09Source Title
European Signal Processing Conference
Print ISSN
2219-5491
Publisher
IEEE
Pages
1193 - 1196
Language
English
Type
Conference PaperItem Usage Stats
79
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11
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Abstract
We study the problem of sequential prediction of real-valued sequences under the squared error loss function. While refraining from any statistical and structural assumptions on the underlying sequence, we introduce a competitive approach to this problem and compare the performance of a sequential algorithm with respect to the large and continuous class of parametric predictors. We define the performance difference between a sequential algorithm and the best parametric predictor as regret, and introduce a guaranteed worst-case lower bounds to this relative performance measure. In particular, we prove that for any sequential algorithm, there always exists a sequence for which this regret is lower bounded by zero. We then extend this result by showing that the prediction problem can be transformed into a parameter estimation problem if the class of parametric predictors satisfy a certain property, and provide a comprehensive lower bound to this case.
Keywords
Lower boundSequential prediction
Worst-case performance
Forecasting
Sequential switching
Signal processing
Parameter estimation problems
Relative performance
Sequential algorithm
Sequential prediction
Squared error loss functions
Structural assumption
Parameter estimation
Permalink
http://hdl.handle.net/11693/27868Published Version (Please cite this version)
https://ieeexplore.ieee.org/document/6952418Collections
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