Comprehensive lower bounds on sequential prediction

Date
2014-09
Advisor
Instructor
Source Title
European Signal Processing Conference
Print ISSN
2219-5491
Electronic ISSN
Publisher
IEEE
Volume
Issue
Pages
1193 - 1196
Language
English
Type
Conference Paper
Journal Title
Journal ISSN
Volume Title
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.

Course
Other identifiers
Book Title
Keywords
Lower bound, Sequential 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
Citation
Published Version (Please cite this version)