Things Bayes can't do
Document type :
Communication dans un congrès avec actes
Title :
Things Bayes can't do
Author(s) :
Conference title :
Proceedings of the 27th International Conference on Algorithmic Learning Theory (ALT'16)
City :
Bari
Country :
Italie
Start date of the conference :
2016-10
Publication date :
2016
HAL domain(s) :
Informatique [cs]/Apprentissage [cs.LG]
Statistiques [stat]/Théorie [stat.TH]
Informatique [cs]/Théorie de l'information [cs.IT]
Statistiques [stat]/Théorie [stat.TH]
Informatique [cs]/Théorie de l'information [cs.IT]
English abstract : [en]
The problem of forecasting conditional probabilities of the next event given the past is consideredin a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct ...
Show more >The problem of forecasting conditional probabilities of the next event given the past is consideredin a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data. Here we show that there are sets C for which such predictors exist, but none of them is a Bayesian predictor with a prior concentrated on C.In other words, there is a predictor with sublinear regret, but every Bayesian predictor must have a linear regret. This negative finding is in sharp contrast with previous resultsthat establish the opposite for the case when one of the predictors in C achieves asymptotically vanishing error.In such a case, if there is a predictor that achieves asymptotically vanishing error for any measure in C, then there is a Bayesian predictor that also has this property, and whose prior is concentrated on (a countable subset of) C.Show less >
Show more >The problem of forecasting conditional probabilities of the next event given the past is consideredin a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data. Here we show that there are sets C for which such predictors exist, but none of them is a Bayesian predictor with a prior concentrated on C.In other words, there is a predictor with sublinear regret, but every Bayesian predictor must have a linear regret. This negative finding is in sharp contrast with previous resultsthat establish the opposite for the case when one of the predictors in C achieves asymptotically vanishing error.In such a case, if there is a predictor that achieves asymptotically vanishing error for any measure in C, then there is a Bayesian predictor that also has this property, and whose prior is concentrated on (a countable subset of) C.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Collections :
Source :
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- http://arxiv.org/pdf/1610.08239
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- 1610.08239
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