DocumentCode :
1410219
Title :
Sequential prediction of individual sequences under general loss functions
Author :
Haussler, David ; Kivinen, Jyrki ; Warmuth, Manfred K.
Author_Institution :
Dept. of Comput. Eng., California Univ., Santa Cruz, CA, USA
Volume :
44
Issue :
5
fYear :
1998
fDate :
9/1/1998 12:00:00 AM
Firstpage :
1906
Lastpage :
1925
Abstract :
We consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function. The goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of (possibly adaptive) prediction strategies, called experts. By using a general loss function, we generalize previous work on universal prediction, forecasting, and data compression. However, here we restrict ourselves to the case when the comparison class is finite. For a given sequence, we define the regret as the total loss on the entire sequence suffered by the adaptive sequential predictor, minus the total loss suffered by the predictor in the comparison class that performs best on that particular sequence. We show that for a large class of loss functions, the minimax regret is either θ(log N) or Ω(√Llog N), depending on the loss function, where N is the number of predictors in the comparison class andL is the length of the sequence to be predicted. The former case was shown previously by Vovk (1990); we give a simplified analysis with an explicit closed form for the constant in the minimax regret formula, and give a probabilistic argument that shows this constant is the best possible. Some weak regularity conditions are imposed on the loss function in obtaining these results. We also extend our analysis to the case of predicting arbitrary sequences that take real values in the interval [0,1]
Keywords :
adaptive systems; binary sequences; data compression; forecasting theory; minimax techniques; prediction theory; probability; adaptive sequential prediction; adaptive sequential predictor; binary sequences; constant; data compression; experts; forecasting; general loss functions; individual sequences; minimax regret; minimax regret formula; performance evaluation; probabilistic argument; regret; universal prediction; Adaptive algorithm; Adaptive coding; Binary sequences; Computer science; Data compression; Minimax techniques; Pattern recognition; Performance loss; US Department of Energy; Writing;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.705569
Filename :
705569
Link To Document :
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